As mentioned by Karan Dua this is now possible in iOS8 using UIApplicationOpenSettingsURLString see Apple's Documentation.

Example:

Swift 4.2

UIApplication.shared.open(URL(string: UIApplication.openSettingsURLString)!)

In Swift 3:

UIApplication.shared.open(URL(string:UIApplicationOpenSettingsURLString)!)

In Swift 2:

UIApplication.sharedApplication().openURL(NSURL(string:UIApplicationOpenSettingsURLString)!)

In Objective-C

[[UIApplication sharedApplication] openURL:[NSURL URLWithString:UIApplicationOpenSettingsURLString]];

Prior to iOS 8:

You can not. As you said this has been covered many times and that pop up asking you to turn on location services is supplied by Apple and not by the App itself. That is why it is able to the open the settings application.

Here are a few related questions & articles:

is it possible to open Settings App using openURL?

Programmatically opening the settings app (iPhone)

How can I open the Settings app when the user presses a button?

iPhone: Opening Application Preferences Panel From App

Open UIPickerView by clicking on an entry in the app's preferences - How to?

Open the Settings app?

iOS: You’re Doing Settings Wrong


From @Yatheeshaless's answer:

You can open settings app programmatically in iOS8, but not in earlier versions of iOS.

Swift:

   UIApplication.sharedApplication().openURL(NSURL(string:UIApplicationOpenSettingsURLString)!)

Swift 4:

if let url = NSURL(string: UIApplicationOpenSettingsURLString) as URL? {
    UIApplication.shared.openURL(url)
}

Swift 4.2 (BETA):

if let url = NSURL(string: UIApplication.openSettingsURLString) as URL? {
    UIApplication.shared.open(url, options: [:], completionHandler: nil)
}

Objective-C:

[[UIApplication sharedApplication] openURL:[NSURL URLWithString:UIApplicationOpenSettingsURLString]];

YES!! you can launch Device Settings screen, I have tested on iOS 9.2

Step 1. we need to add URL schemes

Go to Project settings --> Info --> URL Types --> Add New URL Schemes

enter image description here

Step 2. Launch Settings programmatically Thanks to @davidcann

[[UIApplication sharedApplication] openURL:[NSURL URLWithString:@"prefs://"]];

Also we can launch sub-screens like Music, Location etc. as well by just using proper name

[[UIApplication sharedApplication] openURL:[NSURL URLWithString:@"prefs:root=MUSIC"]];

See this full name list here shared by Henri Normak


Update:

As per the comment everyone wants to know what happens after this change to my application submission status?

So YES!! I got successful update submission and application is available on store without any complain.

Just to confirm, I Just downloaded this morning and disabled Location services, and then started the app, which asked me for location permission and then my alert popup was there to send me on settings -> location services page --> Enabled --> That's it!!

![NOTICE: Your app might be rejected ... even if it's approved it can be rejected in future version if you use this method...]4