Asked by club media how the arrival of former Italy boss Conte at Inter this summer had influenced his decision to move to Serie A, he replied "a lot... he's the best manager in the world"
"He's somebody that can make players better all the time. You can see his record," said Lukaku.
Conte has been a long-time admirer of Lukaku and tried to sign him for Chelsea before the Belgian's move from Everton to United in 2017.
The 26-year-old completed his long-awaited move to Inter on Thursday, joining a club with ambitions of breaking fierce rival Juventus' stranglehold on domestic honours.
Belgium's all-time top scorer with 48 goals, he will be at the centre of Inter's attack, taking the number 9 shirt away from former club captain Mauro Icardi after the Argentina international was frozen out last season following a bitter and public contract row.
He hadn't played a single minute in United's pre-season campaign after being sidelined by Ole Gunnar Solskjaer despite scoring 42 times in all competitions while at Old Trafford.
"I think Inter is a club with a lot of upsides. I think for me it was something I needed," Lukaku said.
"I needed a challenge where I could help a team build for the future. For me, everything is present here to help me and I wish I can help my teammates with my hard work dedication to the game."
Milan-based Gazzetta Dello Sport reports that he will earn €8.5 million a season at Inter, and claims that Inter will pay United an initial €65 million ($73 million) over five years with a further 10 million in potential add-ons, contrasting with reports in Britain that the Premier League club brought in 80 million euros.
They have strengthened a squad that finished fourth in Serie A last season by signing veteran Uruguayan international defender Diego Godin and promising midfielder Nicolo Barella.
Inter are also reportedly close to bringing in Edin Dzeko, with the Bosnian international pushing for the move away from the Italian capital and Roma trying to retain him after failing to find an adequate replacement.
Other targets reportedly include Barcelona's Ivan Rakitic and Lazio star Sergej Milinkovic-Savic, although the club also need to offload Icardi, who is reportedly only interested in a move to Juventus despite interest from Napoli and Roma.