SwiftUI: Send email

@Matteo's answer is good but it needs to use the presentation environment variable. I have updated it here and it addresses all of the concerns in the comments.

import SwiftUI
import UIKit
import MessageUI

struct MailView: UIViewControllerRepresentable {

    @Environment(\.presentationMode) var presentation
    @Binding var result: Result<MFMailComposeResult, Error>?

    class Coordinator: NSObject, MFMailComposeViewControllerDelegate {

        @Binding var presentation: PresentationMode
        @Binding var result: Result<MFMailComposeResult, Error>?

        init(presentation: Binding<PresentationMode>,
             result: Binding<Result<MFMailComposeResult, Error>?>) {
            _presentation = presentation
            _result = result
        }

        func mailComposeController(_ controller: MFMailComposeViewController,
                                   didFinishWith result: MFMailComposeResult,
                                   error: Error?) {
            defer {
                $presentation.wrappedValue.dismiss()
            }
            guard error == nil else {
                self.result = .failure(error!)
                return
            }
            self.result = .success(result)
        }
    }

    func makeCoordinator() -> Coordinator {
        return Coordinator(presentation: presentation,
                           result: $result)
    }

    func makeUIViewController(context: UIViewControllerRepresentableContext<MailView>) -> MFMailComposeViewController {
        let vc = MFMailComposeViewController()
        vc.mailComposeDelegate = context.coordinator
        return vc
    }

    func updateUIViewController(_ uiViewController: MFMailComposeViewController,
                                context: UIViewControllerRepresentableContext<MailView>) {

    }
}

Usage:

import SwiftUI
import MessageUI

struct ContentView: View {

   @State var result: Result<MFMailComposeResult, Error>? = nil
   @State var isShowingMailView = false

    var body: some View {
        Button(action: {
            self.isShowingMailView.toggle()
        }) {
            Text("Tap Me")
        }
        .disabled(!MFMailComposeViewController.canSendMail())
        .sheet(isPresented: $isShowingMailView) {
            MailView(result: self.$result)
        }
    }
}

struct ContentView_Previews: PreviewProvider {
    static var previews: some View {
        ContentView()
    }
}

As you mentioned, you need to port the component to SwiftUI via UIViewControllerRepresentable.

Here's a simple implementation:

struct MailView: UIViewControllerRepresentable {

    @Binding var isShowing: Bool
    @Binding var result: Result<MFMailComposeResult, Error>?

    class Coordinator: NSObject, MFMailComposeViewControllerDelegate {

        @Binding var isShowing: Bool
        @Binding var result: Result<MFMailComposeResult, Error>?

        init(isShowing: Binding<Bool>,
             result: Binding<Result<MFMailComposeResult, Error>?>) {
            _isShowing = isShowing
            _result = result
        }

        func mailComposeController(_ controller: MFMailComposeViewController,
                                   didFinishWith result: MFMailComposeResult,
                                   error: Error?) {
            defer {
                isShowing = false
            }
            guard error == nil else {
                self.result = .failure(error!)
                return
            }
            self.result = .success(result)
        }
    }

    func makeCoordinator() -> Coordinator {
        return Coordinator(isShowing: $isShowing,
                           result: $result)
    }

    func makeUIViewController(context: UIViewControllerRepresentableContext<MailView>) -> MFMailComposeViewController {
        let vc = MFMailComposeViewController()
        vc.mailComposeDelegate = context.coordinator
        return vc
    }

    func updateUIViewController(_ uiViewController: MFMailComposeViewController,
                                context: UIViewControllerRepresentableContext<MailView>) {

    }
}

Usage:

struct ContentView: View {

    @State var result: Result<MFMailComposeResult, Error>? = nil
    @State var isShowingMailView = false

    var body: some View {

        VStack {
            if MFMailComposeViewController.canSendMail() {
                Button("Show mail view") {
                    self.isShowingMailView.toggle()
                }
            } else {
                Text("Can't send emails from this device")
            }
            if result != nil {
                Text("Result: \(String(describing: result))")
                    .lineLimit(nil)
            }
        }
        .sheet(isPresented: $isShowingMailView) {
            MailView(isShowing: self.$isShowingMailView, result: self.$result)
        }

    }

}

(Tested on iPhone 7 Plus running iOS 13 - works like a charm)

Updated for Xcode 11.4

Answers are correct Hobbes the Tige & Matteo

From the comments, if you need to show an alert if no email is set up on the button or tap gesture

@State var isShowingMailView = false
@State var alertNoMail = false
@State var result: Result<MFMailComposeResult, Error>? = nil

HStack {
                Image(systemName: "envelope.circle").imageScale(.large)
                Text("Contact")
            }.onTapGesture {
                MFMailComposeViewController.canSendMail() ? self.isShowingMailView.toggle() : self.alertNoMail.toggle()
            }
                //            .disabled(!MFMailComposeViewController.canSendMail())
                .sheet(isPresented: $isShowingMailView) {
                    MailView(result: self.$result)
            }
            .alert(isPresented: self.$alertNoMail) {
                Alert(title: Text("NO MAIL SETUP"))
            }

To pre-populate To, Body ... also I add system sound same as Apple email sending sound

Parameters: recipients & messageBody can be injected when you init. MailView

import AVFoundation
import Foundation
import MessageUI
import SwiftUI
import UIKit

struct MailView: UIViewControllerRepresentable {
    @Environment(\.presentationMode) var presentation
    @Binding var result: Result<MFMailComposeResult, Error>?
    var recipients = [String]()
    var messageBody = ""

    class Coordinator: NSObject, MFMailComposeViewControllerDelegate {
        @Binding var presentation: PresentationMode
        @Binding var result: Result<MFMailComposeResult, Error>?

        init(presentation: Binding<PresentationMode>,
             result: Binding<Result<MFMailComposeResult, Error>?>)
        {
            _presentation = presentation
            _result = result
        }

        func mailComposeController(_: MFMailComposeViewController,
                                   didFinishWith result: MFMailComposeResult,
                                   error: Error?)
        {
            defer {
                $presentation.wrappedValue.dismiss()
            }
            guard error == nil else {
                self.result = .failure(error!)
                return
            }
            self.result = .success(result)
            
            if result == .sent {
            AudioServicesPlayAlertSound(SystemSoundID(1001))
            }
        }
    }

    func makeCoordinator() -> Coordinator {
        return Coordinator(presentation: presentation,
                           result: $result)
    }

    func makeUIViewController(context: UIViewControllerRepresentableContext<MailView>) -> MFMailComposeViewController {
        let vc = MFMailComposeViewController()
        vc.setToRecipients(recipients)
        vc.setMessageBody(messageBody, isHTML: true)
        vc.mailComposeDelegate = context.coordinator
        return vc
    }

    func updateUIViewController(_: MFMailComposeViewController,
                                context _: UIViewControllerRepresentableContext<MailView>) {}
}

I also improved @Hobbes answer to easily configure parameters like, subject, recipients.

Checkout this gist

Even too lazy to checkout gist, then what about a SPM?

You can now easily copy paste this gift across different projects.

Usage;

import SwiftUI
import MessagesUI
// import SwiftUIEKtensions // via SPM

@State private var result: Result<MFMailComposeResult, Error>? = nil
@State private var isShowingMailView = false

var body: some View {
    Form {
        Button(action: {
            if MFMailComposeViewController.canSendMail() {
                self.isShowingMailView.toggle()
            } else {
                print("Can't send emails from this device")
            }
            if result != nil {
                print("Result: \(String(describing: result))")
            }
        }) {
            HStack {
                Image(systemName: "envelope")
                Text("Contact Us")
            }
        }
        // .disabled(!MFMailComposeViewController.canSendMail())
    }
    .sheet(isPresented: $isShowingMailView) {
        MailView(result: $result) { composer in
            composer.setSubject("Secret")
            composer.setToRecipients(["[email protected]"])
        }
    }
}