How do you add CloudFront in front of API Gateway

API Gateway (APIG), while it uses CloudFront (CF) it does not support CDN edge caching. When I configured a CF distribution to use APIG as the custom origin, I get a permission denied error.

How do I configure CF to fix this?

Until API Gateway (APIG) supports edge caching via its internal use of CloudFront (CF), I have come up with a workaround.

You can indeed put CF dist in front of APIG, the trick is to force HTTPS only "Viewer Protocol Policy" AND to NOT forward the HOST header because APIG needs SNI.

I setup my CF "Default Cache Behavior Settings" to not forward any headers, and forced "Viewer Protocol Policy" to "HTTPS Only" and it works. Hope this helps others.

Here is a CloudFormation resource object that has all the required configuration (Note: I use the convention <stage>--<app name> for StackName):

CloudFront:  
    Type: AWS::CloudFront::Distribution
    Properties:
      DistributionConfig:
        Enabled: true
        IPV6Enabled: true
        HttpVersion: http2
        Comment: !Join [ '--', [!Ref 'AWS::StackName', ' Cloud Front']]
        Aliases: [!Ref CloudFrontCname]
        ViewerCertificate:
          AcmCertificateArn: !Ref AcmCertificateArn
          SslSupportMethod: sni-only
          MinimumProtocolVersion: TLSv1.1_2016
        Origins:
        - Id: APIGOrigin
          DomainName: !Sub
            - ${apigId}.execute-api.${AWS::Region}.amazonaws.com
            - { apigId: !Ref ApiGatewayLambdaProxy }
          OriginPath: !Sub
            - /${Stage}
            - { Stage: !Select [ "0", !Split [ '--', !Ref 'AWS::StackName' ] ] }
          CustomOriginConfig:
            # HTTPPort: 80
            HTTPSPort: 443
            OriginProtocolPolicy: https-only
          OriginCustomHeaders:
            - HeaderName: 'Verify-From-Cf'
              HeaderValue: !Ref VerifyFromCfHeaderVal
        DefaultCacheBehavior:
          AllowedMethods: ["DELETE", "GET", "HEAD", "OPTIONS", "PATCH", "POST", "PUT"]
          CachedMethods: ["GET", "HEAD", "OPTIONS"]
          ForwardedValues:
            Headers:
            - Access-Control-Request-Headers
            - Access-Control-Request-Method
            - Origin
            - Authorization
            # - Host APIG needs to use SNI
            QueryString: true
          TargetOriginId: APIGOrigin
          ViewerProtocolPolicy: https-only
          Compress: true
          DefaultTTL: 0
        CustomErrorResponses:
        - ErrorCachingMinTTL: 0
          ErrorCode: 400
        - ErrorCachingMinTTL: 1
          ErrorCode: 403
        - ErrorCachingMinTTL: 5
          ErrorCode: 500
  DNSARecord:    
    Type: AWS::Route53::RecordSet
    Properties:
      Comment: !Ref 'AWS::StackName'
      Name: !Ref CloudFrontCname
      Type: A
      HostedZoneName: !Join ['.', [ !Select [1, !Split ['.', !Ref CloudFrontCname]], !Select [2, !Split ['.', !Ref CloudFrontCname]], '']]
      AliasTarget:
        HostedZoneId: !Ref Route53HostedZoneId
        DNSName: !GetAtt CloudFront.DomainName
  DNSAAAARecord:    
    Type: AWS::Route53::RecordSet
    Properties:
      Comment: !Ref 'AWS::StackName'
      Name: !Ref CloudFrontCname
      Type: AAAA
      HostedZoneName: !Join ['.', [ !Select [1, !Split ['.', !Ref CloudFrontCname]], !Select [2, !Split ['.', !Ref CloudFrontCname]], '']]
      AliasTarget:
        HostedZoneId: !Ref Route53HostedZoneId
        DNSName: !GetAtt CloudFront.DomainName

Late 2018 updates

• CloudFormation finally supports setting SSL proto ver: MinimumProtocolVersion: TLSv1.1_2016
• I've baked this (and many other) best practices into an OSS project: aws-blueprint

Adding to previous answers:

it's important that behavior path pattern is actually something that matches "real" path.

If API endpoint is <id>.execute-api.<region>.amazonaws.com/stage-name/my-api

And origin domain + path is <id>.execute-api.<region>.amazonaws.com/stage-name

Behavior path pattern has to be my-api, my-api/*, my-api/something, etc

I don't know why, but I thought that path pattern can be used as alias, for example:

https://www.example.com/random-name (path pattern random-name) resolves to domain + path set in origin, e.g <id>.execute-api.<region>.amazonaws.com/stage-name.

That's not the case.

If API Gateway returns a 403 error with:

Authorization header requires 'Credential' parameter. Authorization header requires 'Signature' parameter. Authorization header requires 'SignedHeaders' parameter. Authorization header requires existence of either a 'X-Amz-Date' or a 'Date' header.

it can also be that the origin endpoint is incorrect. "API Gateway treats all errors to non-existent paths as 403 permission denied errors rather than a 404 not found error." (see this support thread).

I got this error and assumed I was incorrectly forwarding the Authorization header, but I had simply misconfigured the origin path.

I just want to reiterate here, for anyone who's following the guide from AWS premium support knowledge center,

How do I set up API Gateway with my own CloudFront distribution? https://aws.amazon.com/premiumsupport/knowledge-center/api-gateway-cloudfront-distribution/

If you are using AWS console to set up the CloudFront distribution, the root cause is that you set Cache Based on Selected Request Headers to all.

Setting it to None or exclude the Host header in the Whitelist would solve the problem.