Owner Aurelio De Laurentiis confirmed the deal, worth a reported 30 million euros (£25.2 million), on social media by saying "Welcome Romelu" with a photo of him signing his three-year contract.
Lukaku's move to Napoli keeps him in Italy, at his third club in as many years after loan spells at Inter Milan and Roma.
He was the idol of Inter fans when he fired their team to the Serie A title in 2021 under new Napoli coach Antonio Conte before being sold for well over 100 million euros (£84.1m) to Chelsea that summer.
But Lukaku flopped on his return to Stamford Bridge, and that massive fee left him in limbo as clubs refused to meet the Premier League club's valuations for a sale.
It led to an underwhelming year on loan back at Inter in the 2022/23 season during which he was dogged by injury and largely kept out of the team by Edin Dzeko.
His mooted permanent move to Inter broke down last summer as the club found out he had been making noises towards fierce rivals AC Milan and Juventus, so Lukaku and Chelsea eventually accepted another loan deal with Roma.
However Roma were not interested in shelling out for Lukaku, allowing Napoli coach Antonio Conte to be reunited with a striker whose reputation has suffered in recent years but is still Belgium's all-time top scorer with 85 goals in 119 appearances.
