Lukaku officially joined the Red Devils on a five-year contract earlier this week after the 20-time English champions agreed a deal, believed to be in the region of £75m, with Everton.
Mourinho managed Lukaku while the pair were at Chelsea, but the Portuguese has revealed that it was Man United's executive vice-chairman Ed Woodward that handled the majority of the transfer.
"Hopefully [he will bring] goals, he's the kind of player that everybody knows, he's a striker so we're not speaking about a multi-functional player or create doubts about positions on the pitch, he's a striker and normally strikers score goals," Mourinho told reporters.
"The reason why he was so important and difficult to get is what he did in the Premier League because obviously there are other good strikers in football but the Premier League is a very specific habitat, a different habitat, normally they need some time to adapt and Lukaku plays in Premier League for the last four or five seasons.
"I didn't negotiate, it was Mr Woodward who negotiated with Romelu, his agent and the Everton board, the only thing I did was to call him when the situation was almost there just to guarantee him that he would be an important player in my team.
"It's quite a great experience the fact we worked together already for a few months and during the time when I was at Chelsea and when he was at Everton our relationship was always very close despite it not working well for us together. He's intelligent, he's polite, we kept the contact, the feeling and now we are back together in different moments and I have no doubts it is going to work."
Lukaku could make his Man United debut against Los Angeles Galaxy on Saturday night.