Owen completed a surprise switch to Old Trafford on Friday night just two days after he became a free agent when his contract at Newcastle expired.
Rush told Sky Sports News: "It's a chance for Michael to get back and score some goals. He'll get chances for Manchester United and will score goals."
Injuries have ruined recent seasons for Owen and the England striker made just 71 league appearances for the Magpies since his move from Real Madrid in 2005.
However, Rush believes the move gives Owen an opportunity to return to form in front of goal after scoring just 30 times in all competitions in the north-east.
The former Wales forward added: "People have knocked Michael Owen all his career but he comes back bigger and better.
"People said he was finished years ago but he's a fantastic player who comes back stronger and better.
"It (the talk) won't worry him, I know the way he is and he doesn't have to prove anything anyway."
Former Liverpool favourite Rush - who scored more than 220 goals for the club in two spells either side of an ill-fated stint in Italy with Juventus - believes Owen would make a good impression were he to return to Anfield.
However, the 47-year-old added: "Personally, I'd like to have seen him at Liverpool but they haven't lost their best strikers. He (manager Rafael Benitez) will be happy with what he's got."