The Belgian striker became Manchester United’s second signing of the summer last week when he joined the Red Devils from Everton, despite having been linked with Chelsea for much of the season.
Rooney, meanwhile, ended up moving in the opposite direction when he returned to his boyhood club Everton last week.
The veteran forward knows all about the pressures of representing Manchester United, having enjoyed a hugely successful career at Old Trafford.
And Rooney has sent a message of support for Lukaku after he signed for the Red Devils last week.
Rooney is quoted as saying by the Daily Express: “Playing for Manchester United is a test of character as well as your ability. You have got to be strong enough mentally to accept the challenge.
“United are a football club which demands success. Romelu has to be strong enough to take up that challenge. If he does that, then with the ability he’s got he will be a success. If he doesn’t, if he worries about things, then it will be more difficult.”
Manchester United have so far only signed Lukaku and defender Victor Lindelof from Benfica so far this summer as Jose Mourinho prepares his team for a return to the Champions League next season.
The Red Devils finished sixth in the Premier League but won the EFL Cup and Europa League last term.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news