How to animate Tab bar tab switch with a CrossDissolve slide transition?

There is a simpler way to doing this. Add the following code in the tabbar delegate:

Working on Swift 2, 3 and 4

class MySubclassedTabBarController: UITabBarController {

    override func viewDidLoad() {
      super.viewDidLoad()
      delegate = self
    }
}

extension MySubclassedTabBarController: UITabBarControllerDelegate  {
    func tabBarController(_ tabBarController: UITabBarController, shouldSelect viewController: UIViewController) -> Bool {

        guard let fromView = selectedViewController?.view, let toView = viewController.view else {
          return false // Make sure you want this as false
        }

        if fromView != toView {
          UIView.transition(from: fromView, to: toView, duration: 0.3, options: [.transitionCrossDissolve], completion: nil)
        }

        return true
    }
}

EDIT (4/23/18) Since this answer is getting popular, I updated the code to remove the force unwraps, which is a bad practice, and added the guard statement.

EDIT (7/11/18) @AlbertoGarcía is right. If you tap the tabbar icon twice you get a blank screen. So I added an extra check

If you want to use UIViewControllerAnimatedTransitioning to do something more custom than UIView.transition, take a look at this gist.

// MyTabController.swift

import UIKit

class MyTabBarController: UITabBarController {

    override func viewDidLoad() {
        super.viewDidLoad()
        delegate = self
    }
}

extension MyTabBarController: UITabBarControllerDelegate {

    func tabBarController(_ tabBarController: UITabBarController, animationControllerForTransitionFrom fromVC: UIViewController, to toVC: UIViewController) -> UIViewControllerAnimatedTransitioning? {
        return MyTransition(viewControllers: tabBarController.viewControllers)
    }
}

class MyTransition: NSObject, UIViewControllerAnimatedTransitioning {

    let viewControllers: [UIViewController]?
    let transitionDuration: Double = 1

    init(viewControllers: [UIViewController]?) {
        self.viewControllers = viewControllers
    }

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

    func animateTransition(using transitionContext: UIViewControllerContextTransitioning) {

        guard
            let fromVC = transitionContext.viewController(forKey: UITransitionContextViewControllerKey.from),
            let fromView = fromVC.view,
            let fromIndex = getIndex(forViewController: fromVC),
            let toVC = transitionContext.viewController(forKey: UITransitionContextViewControllerKey.to),
            let toView = toVC.view,
            let toIndex = getIndex(forViewController: toVC)
            else {
                transitionContext.completeTransition(false)
                return
        }

        let frame = transitionContext.initialFrame(for: fromVC)
        var fromFrameEnd = frame
        var toFrameStart = frame
        fromFrameEnd.origin.x = toIndex > fromIndex ? frame.origin.x - frame.width : frame.origin.x + frame.width
        toFrameStart.origin.x = toIndex > fromIndex ? frame.origin.x + frame.width : frame.origin.x - frame.width
        toView.frame = toFrameStart

        DispatchQueue.main.async {
            transitionContext.containerView.addSubview(toView)
            UIView.animate(withDuration: self.transitionDuration, animations: {
                fromView.frame = fromFrameEnd
                toView.frame = frame
            }, completion: {success in
                fromView.removeFromSuperview()
                transitionContext.completeTransition(success)
            })
        }
    }

    func getIndex(forViewController vc: UIViewController) -> Int? {
        guard let vcs = self.viewControllers else { return nil }
        for (index, thisVC) in vcs.enumerated() {
            if thisVC == vc { return index }
        }
        return nil
    }
}