class ViewController: UIViewController {

@IBOutlet weak var imageView: UIImageView!
override func viewDidLoad() {
    super.viewDidLoad()
    // create tap gesture recognizer
    let tapGesture = UITapGestureRecognizer(target: self,action: "imageTapped:")

    // add it to the image view;
    imageView.addGestureRecognizer(tapGesture)
    // make sure imageView can be interacted with by user
    imageView.userInteractionEnabled = true
}

func imageTapped(gesture: UIGestureRecognizer) {
    // if the tapped view is a UIImageView then set it to imageview
    if let imageView = gesture.view as? UIImageView {
        println("Image Tapped")
        //Here you can initiate your new ViewController

        }
    }
}

Swift 3.0

class ViewController: UIViewController {

    @IBOutlet weak var imageView: UIImageView!
    override func viewDidLoad() {
        super.viewDidLoad()
        // create tap gesture recognizer
        let tapGesture = UITapGestureRecognizer(target: self,action: #selector(ViewController.imageTapped(gesture:)))

        // add it to the image view;
        imageView.addGestureRecognizer(tapGesture)
        // make sure imageView can be interacted with by user
        imageView.isUserInteractionEnabled = true
    }

    func imageTapped(gesture: UIGestureRecognizer) {
        // if the tapped view is a UIImageView then set it to imageview
        if (gesture.view as? UIImageView) != nil {
            print("Image Tapped")
            //Here you can initiate your new ViewController

        }
    }
}