UIButton uses an old objective-c style method to add new callbacks which requires selectors. If you would rather use a block based approach then consider the following approach. You can specify a swift closure to be executed when the button receives a touch event.

UIButtonCalbackExtension.swift

///////////////
// code example
//-------------
button.callback { _ in 
	print("hello world") // print "hello world" when touchUpInside event is recieved
}

button.callback(for: [.TouchDown]) { _ in
	print("hello world") // print "hello world" when touchDownInside event is recieved
}
		
button.callback(for: [.TouchUpInside, .TouchDown]) { _ in
	print("hello world2") // print "hello world2" when touchUpInside OR touchDownInside event are recieved
}

////////
// code
//------
extension UIButton {
	
	// a proxy class
	internal class DHTargetActionProxy: UIView {
		// a block that will be called
		internal var _action: (AnyObject) -> ()
		
		internal init(controlEvents: UIControlEvents, action: (AnyObject) -> ()) {
			_action = action
			super.init(frame: CGRect.zero)
			self.tag = Int(controlEvents.rawValue)
		}
		
		internal required init?(coder aDecoder: NSCoder) {
			fatalError("init(coder:) has not been implemented")
		}
		
		internal func action(sender: AnyObject) {
			_action(sender)
		}
	}
	
	public func callback(`for`controlEvents: UIControlEvents = [UIControlEvents.TouchUpInside],
	                    action: (AnyObject) -> ())
	{
		// An array of supported touch events
		let ctrlEvts: [UIControlEvents] =
		[
			.TouchDown,
			.TouchDownRepeat,
			.TouchDragInside,
			.TouchDragOutside,
			.TouchDragEnter,
			.TouchDragExit,
			.TouchUpInside,
			.TouchUpOutside,
			.TouchCancel,
			
			.ValueChanged,
			.EditingDidBegin,
			.EditingChanged,
			.EditingDidEnd,
			.EditingDidEndOnExit
		]
		
		ctrlEvts.forEach {
			if controlEvents.contains($0) {
				// each touch event requires its own proxy object
				_addActionToView($0.rawValue, action: action)
			}
		}
	}
	
	private func _addActionToView(tag: UInt, action: (AnyObject) -> ()) {
		let foo = DHTargetActionProxy(controlEvents: UIControlEvents(rawValue: tag), action: action)
		
		// remove previous if it exists
		viewWithTag(Int(tag))?.removeFromSuperview()
		
		// since foo is not retained by target(_, action:, forControlEvents:) we must save it somewhere.  This implementation saves it as a subview.
		self.addSubview(foo)
		
		// add target to button.  Target instance is a proxy object and it calls a selector beloing to that proxy object.
		addTarget(foo, action: #selector(DHTargetActionProxy.action(_:)), forControlEvents: UIControlEvents(rawValue: tag))
	}
	
}