The Nerazzurri coasted to their first Scudetto since the 2009-2010 campaign as they clinched the title with four games to spare, courtesy of a 20-game unbeaten run at the end of the season.
Despite Conte's title-winning campaign, the Italian head coach left by mutual consent in May before Inzaghi, who was previously at Lazio, was appointed at San Siro.
And after returning to Italy following Belgium's Euro 2020 semi-final exit, Lukaku, who scored 24 times in 36 league outings while also providing 11 assists in 2020-2021, revealed how hungry he is to work with Inzaghi towards further success.
"We had a good chat on the day that the club announced that he was going to be the new coach and we also spoke when I was at the Euros," Lukaku said.
"My brother has also told me plenty about him. He's a good coach. I think he’ll help the team achieve so much.
"We hope we can all work together to continue down the path that we've started."
Only in 2016-2017 at Everton did the forward (25 goals) score more times in one of Europe's top-five leagues than last season and the Belgian promised to chase more silverware in 2021-2022.
"We now have a few weeks to prepare as well as we can for the new campaign," the 28-year-old said. "We hope to do well and achieve even more than last year.
"I’m thrilled to be back. We hope to continue down the path that we’ve started and to keep winning. All the players will work hard to make your dreams come true."
Inter gets its title defence underway at home to Genoa on 22 August (AEST) after facing Atletico Madrid on 7 August in its final pre-season friendly.