While not in any way a formal apology, former U.S. President George W. Bush did admit that the invasion of Iraq was unjustified.
...the decision of one man to launch a wholly unjustified and brutal invasion of Iraq. I mean, of Ukraine. Iraq too. Anyway. 75...
The topic he was talking about leading up to that statement was about the Russian invasion of Ukraine, so it sounds like he originally said "Iraq" by mistake. Even so, while he very well may have never intended to mention Iraq and originally said it accidentally, there is a noticeable pause between when he says "I mean of Ukraine" and "Iraq too", indicating that he does indeed believe that Iraq was also unjustly invaded. This is further cemented by his shrug and nodding, as can be seen in the video.
Nonetheless, his statements don't appear to meet the dictionary definition of an apology and no branch of the U.S. government has issued an apology (and as far as I'm aware, no formal apology has been issued by any branch of government of any of the U.S.' allies in the invasion.)
EDIT: some say in the comments it was just a gaffe. Supposedly he has told his advisers that the world is better off without Saddam Hussein and that he has not changed his mind about that, so they very well may be correct.