Lukakau explained when he knew his Manchester United time was over, working with "unique" Antonio Conte and repaying the €65m fee with goals.
The striker gave an interview to the Corriere dello Sport and spoke on an array of topics.
"I've dreamed of Inter for some time. I loved Ronaldo and Adriano, but it was Ibra that taught me everything, especially in our talks on the team bus. I believe he will return to Serie A."
"Immobile is also a great striker. I first learned to speak Italian whilst watching my brother Jordan playing for Lazio on TV. Once I learned that [Ole Gunnar] Solsjkaer planned to put me on the wing, then I knew my time at Manchester United was over."
Talk then turned to the scudetto, with Inter currently battling it out with Juve at the top of the table.
"Better to be silent [on talk of the title]. Many think they can beat Juve, but in fact no one has done it for eight years. We have to take one game at at time."
"I don't mind being the most expensive player in Inter's history, nor replacing Icardi, who give a lot here in Milan. When I arrived, Mauro was very nice and kind to me. I wish him all the best at Paris-Saint Germain and hope he wins there. We are two different forwards.
"It would be nice to be Capocannoniere, but I'm not the type of player who says I want this or that individual title. I think of the team first. My biggest motivation is helping the team, and to help the team we score goals.
"So far everything has been fine, but I want to do better by working to the maximum every day in training. Now I'm at 100%, but I don't stop, I want to show Inter that they decided well in signing me."