United's all-time leading goalscorer Rooney — now back playing for boyhood club Everton — believes Sanchez can help inspire the Red Devils, who have not won the title since Alex Ferguson's final season in 2012-13.
"For me, he's the perfect player for Manchester United. He's got aggression, he's got passion, desire and you can see he's a winner," Rooney told Sky Sports.
"They are the players you want, almost like when [Carlos] Tevez joined United [from West Ham in 2007].
"Them players lift the other players and get an extra 10 per cent of the players around him. I think Alexis Sanchez will do that."
Lukaku also scored against Huddersfield at Old Trafford, taking his season tally to 12 goals in the Premier League after his £75 million arrival from Everton.
The Belgium international striker has been criticised for some of his performances this term, but Rooney feels Sanchez's presence will ease the burden on Lukaku.
"I think that's what Manchester United have lacked, players around Lukaku who are going to push Lukaku on as well and try help him get a bit more freedom and score more goals," Rooney added.
Sanchez's deal involved out-of-favour playmaker Henrikh Mkhitaryan moving in the opposite direction to Arsenal.
The Armenia star has hit the ground running at the Emirates Stadium, providing three assists in Arsenal's 5-1 rout of Everton.
"I think at Manchester United he didn't get the freedom he really wanted to go and perform, that he had at Dortmund and that style of play that Dortmund played," Rooney said.
"And at Arsenal he'll have players round him running off the ball, taking the ball and he'll create goals and score goals. I really do think he'll kick on."