Financial details were not revealed but British media reported Napoli paid Stg 30 million ($A58m) for the 31-year-old.
Lukaku returned to Chelsea in 2021 for Stg 97.5m ($A188.9m) but spent the last two seasons on loan in Italy, with Inter and AS Roma.
Chelsea also loaned goalkeeper Kepa Arrizabalaga to Bournemouth until the end of the season.
Kepa spent last season on loan at Real Madrid and became available for a move after being told he was not in new manager Enzo Maresca's first-team plans for the current campaign.
The Spain international, who is the world's most expensive keeper following his Stg 71m ($A138m) transfer from Athletic Bilbao in 2018, has signed a one-year contract extension with the Blues.
Chelsea's clear-out continued with midfielder Tino Anjorin's moving to Serie A side Empoli on a three-year deal.
Raheem Sterling is also set to leave Stamford Bridge with several clubs interested, though his wages are an issue.
Also on Thursday Liverpool completed the signing of Italy forward Federico Chiesa from Juventus on a long-term contract
Juventus said the deal was worth 12m euros ($A20 million) plus 3m euros(A$5m) in add-ons for the 26-year-old, who scored 32 goals in 131 appearances for them in four seasons at the club.
"I'm so happy to be a Liverpool player," Chiesa said in a statement. "I said yes immediately because I know the history of this club, I know what it represents to the fans."
Everton manager Sean Dyche has confirmed Neal Maupay is set to leave while a deal to sign Orel Mangala from Lyon is edging closer.
French striker Maupay, who spent last season on loan at Brentford and has been restricted to just 12 Premier League starts since arriving from Brighton in the summer of 2022, is bound for Marseille.
Ajax have announced the signing of Netherlands striker Wout Weghorst from Championship club Burnley.
Weghorst, 32, has agreed a deal with Ajax until June 2026 for an undisclosed fee.
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