The Red Devils signed Lukaku from Everton in the summer transfer window. Rooney, who is United's all-time leading goalscorer, returned to Goodison Park and has already scored twice for Ronald Koeman's side.
"For that Manchester United side, he [Lukaku] is the perfect player. He is powerful, quick and strong and he scores goals, so certainly will improve that team," Rooney told talkSPORT.
Mourinho has fielded Lukaku to lead the 20-time English champions' attack. The 24-year-old has already scored four goals in all competitions for United, which includes three goals in the Premier League.
United won the EFL Cup and Europa League last season, and they finished sixth in the league. It was the Portuguese tactician's first season at Old Trafford and Rooney remains confident that Mourinho will bring success to the club.
"Jose came in and last season in the league we struggled and weren't consistent enough. Obviously in the cups United did well. I could see where Jose was going with the team and they will be a big success," he said.
Mourinho replaced Louis van Gaal as United's manager last summer. The Dutchman was allowed to leave the club just days after he guided the Red Devils to the FA Cup triumph in May 2016. Rooney believes United would have further improved, if Van Gaal was still in charge at the club last season.
"He (Van Gaal) got a lot of stick. I believe if he stayed it would have got better. He looked at all the small details not only off the pitch but on the pitch," the former United star explained.
"I think the one thing he did was keep the standards with the players, he was demanding the best from you every day. We used to film the training sessions, sit back and watch the training sessions back. It was tough for the players in that aspect but if he stayed we would have got better."