How to present view controller from right to left in iOS using Swift

You can also use custom segue.

Swift 5

class SegueFromRight: UIStoryboardSegue {

    override func perform() {
        let src = self.source
        let dst = self.destination

        src.view.superview?.insertSubview(dst.view, aboveSubview: src.view)
        dst.view.transform = CGAffineTransform(translationX: src.view.frame.size.width, y: 0)

        UIView.animate(withDuration: 0.25,
               delay: 0.0,
               options: UIView.AnimationOptions.curveEaseInOut,
               animations: {
                    dst.view.transform = CGAffineTransform(translationX: 0, y: 0)
            },
                   completion: { finished in
                    src.present(dst, animated: false, completion: nil)
        })
    }
}

Read up all answers and can't see correct solution. The right way do to so is to make custom UIViewControllerAnimatedTransitioning for presented VC delegate.

So it assumes to make more steps, but the result is more customizable and haven't some side effects, like moving from view together with presented view.

So, assume you have some ViewController, and there is a method for presenting

var presentTransition: UIViewControllerAnimatedTransitioning?
var dismissTransition: UIViewControllerAnimatedTransitioning?    

func showSettings(animated: Bool) {
    let vc = ... create new vc to present

    presentTransition = RightToLeftTransition()
    dismissTransition = LeftToRightTransition()

    vc.modalPresentationStyle = .custom
    vc.transitioningDelegate = self

    present(vc, animated: true, completion: { [weak self] in
        self?.presentTransition = nil
    })
}

presentTransition and dismissTransition is used for animating your view controllers. So you adopt your ViewController to UIViewControllerTransitioningDelegate:

extension ViewController: UIViewControllerTransitioningDelegate {
    func animationController(forPresented presented: UIViewController, presenting: UIViewController, source: UIViewController) -> UIViewControllerAnimatedTransitioning? {
        return presentTransition
    }

    func animationController(forDismissed dismissed: UIViewController) -> UIViewControllerAnimatedTransitioning? {
        return dismissTransition
    }
}

So the last step is to create your custom transition:

class RightToLeftTransition: NSObject, UIViewControllerAnimatedTransitioning {
    let duration: TimeInterval = 0.25

    func transitionDuration(using transitionContext: UIViewControllerContextTransitioning?) -> TimeInterval {
        return duration
    }

    func animateTransition(using transitionContext: UIViewControllerContextTransitioning) {
        let container = transitionContext.containerView
        let toView = transitionContext.view(forKey: .to)!

        container.addSubview(toView)
        toView.frame.origin = CGPoint(x: toView.frame.width, y: 0)

        UIView.animate(withDuration: duration, delay: 0, options: .curveEaseOut, animations: {
            toView.frame.origin = CGPoint(x: 0, y: 0)
        }, completion: { _ in
            transitionContext.completeTransition(true)
        })
    }
}

class LeftToRightTransition: NSObject, UIViewControllerAnimatedTransitioning {
    let duration: TimeInterval = 0.25

    func transitionDuration(using transitionContext: UIViewControllerContextTransitioning?) -> TimeInterval {
        return duration
    }

    func animateTransition(using transitionContext: UIViewControllerContextTransitioning) {
        let container = transitionContext.containerView
        let fromView = transitionContext.view(forKey: .from)!

        container.addSubview(fromView)
        fromView.frame.origin = .zero

        UIView.animate(withDuration: duration, delay: 0, options: .curveEaseIn, animations: {
            fromView.frame.origin = CGPoint(x: fromView.frame.width, y: 0)
        }, completion: { _ in
            fromView.removeFromSuperview()
            transitionContext.completeTransition(true)
        })
    }
}

In that code view controller is presented over current context, you can make your customizations from that point. Also you may see custom UIPresentationController is useful as well (pass in using UIViewControllerTransitioningDelegate)

Complete code for present/dismiss, Swift 3

extension UIViewController {

    func presentDetail(_ viewControllerToPresent: UIViewController) {
        let transition = CATransition()
        transition.duration = 0.25
        transition.type = kCATransitionPush
        transition.subtype = kCATransitionFromRight
        self.view.window!.layer.add(transition, forKey: kCATransition)

        present(viewControllerToPresent, animated: false)
    }

    func dismissDetail() {
        let transition = CATransition()
        transition.duration = 0.25
        transition.type = kCATransitionPush
        transition.subtype = kCATransitionFromLeft
        self.view.window!.layer.add(transition, forKey: kCATransition)

        dismiss(animated: false)
    }
}

It doesn't matter if it is xib or storyboard that you are using. Normally, the right to left transition is used when you push a view controller into presentor's UINavigiationController.

UPDATE

Added timing function kCAMediaTimingFunctionEaseInEaseOut

Sample project with Swift 4 implementation added to GitHub

Swift 3 & 4.2

let transition = CATransition()
transition.duration = 0.5
transition.type = CATransitionType.push
transition.subtype = CATransitionSubtype.fromRight
transition.timingFunction = CAMediaTimingFunction(name:CAMediaTimingFunctionName.easeInEaseOut)
view.window!.layer.add(transition, forKey: kCATransition)
present(dashboardWorkout, animated: false, completion: nil)

ObjC

CATransition *transition = [[CATransition alloc] init];
transition.duration = 0.5;
transition.type = kCATransitionPush;
transition.subtype = kCATransitionFromRight;
[transition setTimingFunction:[CAMediaTimingFunction functionWithName:kCAMediaTimingFunctionEaseInEaseOut]];
[self.view.window.layer addAnimation:transition forKey:kCATransition];
[self presentViewController:dashboardWorkout animated:false completion:nil];

Swift 2.x

let transition = CATransition()
transition.duration = 0.5
transition.type = kCATransitionPush
transition.subtype = kCATransitionFromRight
transition.timingFunction = CAMediaTimingFunction(name:kCAMediaTimingFunctionEaseInEaseOut)
view.window!.layer.addAnimation(transition, forKey: kCATransition)
presentViewController(dashboardWorkout, animated: false, completion: nil)

Seems like the animated parameter in the presentViewController method doesn't really matter in this case of custom transition. It can be of any value, either true or false.