Create a button programmatically and set a background image

SWIFT 3 Version of Alex Reynolds' Answer

let image = UIImage(named: "name") as UIImage?
let button = UIButton(type: UIButtonType.custom) as UIButton
button.frame = CGRect(x: 100, y: 100, width: 100, height: 100)
button.setImage(image, for: .normal)
button.addTarget(self, action: Selector("btnTouched:"), for:.touchUpInside)
        self.view.addSubview(button)

Try below:

let image = UIImage(named: "ImageName.png") as UIImage
var button   = UIButton.buttonWithType(UIButtonType.System) as UIButton
button.frame = CGRectMake(100, 100, 100, 100)
button .setBackgroundImage(image, forState: UIControlState.Normal)
button.addTarget(self, action: "Action:", forControlEvents:UIControlEvents.TouchUpInside)
menuView.addSubview(button)

Let me know whether if it works or not?

Your code should look like below

let image = UIImage(named: "name") as UIImage?
let button   = UIButton(type: UIButtonType.Custom) as UIButton
button.frame = CGRectMake(100, 100, 100, 100)
button.setImage(image, forState: .Normal)
button.addTarget(self, action: "btnTouched:", forControlEvents:.TouchUpInside)
self.view.addSubview(button)

Swift 5 version of accepted answer:

let image = UIImage(named: "image_name")
let button = UIButton(type: UIButton.ButtonType.custom)
button.frame = CGRect(x: 100, y: 100, width: 200, height: 100)
button.setImage(image, for: .normal)
button.addTarget(self, action: #selector(function), for: .touchUpInside)

//button.backgroundColor = .lightGray
self.view.addSubview(button)

where of course

@objc func function() {...}

The image is aligned to center by default. You can change this by setting button's imageEdgeInsets, like this:

// In this case image is 40 wide and aligned to the left
button.imageEdgeInsets = UIEdgeInsets(top: 5, left: 5, bottom: 5, right: button.frame.width - 45)