The Belgian striker secured a £97.5m return to Stamford Bridge last summer from Inter.
But it was a miserable campaign for the 29-year-old as he mustered only 16 Premier League starts.
The deal is believed to be worth £7m, although Inter do not have a clause or obligation to buy.
After arriving in Milan on Wednesday morning, Lukaku told reporters: "I'm happy to be here."
Lukaku scored 24 Serie A goals during the 2020/21 season as Inter ended an 11-year wait to claim the Scudetto.