Is it possible to push a View Controller with a completion block?

The better solution would be wrapping the push animation by an CATransaction and set the completionBlock. There's no need to deal with timings.

[CATransaction begin];
[CATransaction setCompletionBlock:^{
    //whatever you want to do after the push
}];
[[self navigationController] pushViewController:viewController animated:YES];
[CATransaction commit];

justMartin's answer worked great for me. For those new to using swift API:

CATransaction.begin()
navigationController?.pushViewController(viewController, animated: true)
CATransaction.setCompletionBlock({ 
    //your post animation logic
})
CATransaction.commit()

Not sure if I understand correctly, but I pushed a view controller in a completion block as follows. In a table view controller, added the following line to the header file:

typedef void(^myCompletion)(BOOL);

Then in the class itself, added the following method:

-(void) myMethod:(myCompletion) compblock
{
    compblock(YES);
}

Now in didSelectRowAtIndexPath, I called myMethod and in the completion block, pushed a view controller.

[self myMethod:^(BOOL finished) {
    if(finished){
        dispatch_async(dispatch_get_main_queue(), ^{
            DVSecondTableViewController *vc = [[DVSecondTableViewController alloc] init];
            [self.navigationController pushViewController:vc animated:YES];
        });
    }
}];

I'm not sure if it's okay to push view controllers outside of the main thread, so I embedded that call in a dispatch_async().

Solution with CATransaction is great but there is another way to do that. You can make your controller a delegate of UINavigationController and implement didShowViewController method:

class FooBarController: UIViewController, UINavigationControllerDelegate {
  func viewDidLoad() {
    self.navigationController?.delegate = self
  }

  func navigationController(navigationController: UINavigationController, didShowViewController viewController: UIViewController, animated: Bool) {
    // your awesome completion code here 
  }
}

This approach can be more convenient for your task