Delph initially made public his commitment to Villa and his wish to stay at the club early last week, but was officially announced as a City player on Friday, after completing an £8million transfer.
The move invited the wrath of Villa fans, but former Villans teammate Given believes Delph now has a real opportunity to compete for titles at his new club.
"I think Fabian's a great player and he deserves a crack at a team that's going to challenge for the Premier League and he will do that at Man City," Given, who also played spent two years at City, told Sky Sports News HQ.
"They've got a great set of players, I think he's happy he made it (the decision) now.
"People will probably question why he said he wasn't going and was going but it just shows that players are human beings at the end of the day and they can change their mind.
"I think in the end he's made the right decision because it's an opportunity to go and challenge for the Premier League title at Manchester City and opportunities don't always come along in your career."