The 31-year-old made 177 appearances in all competitions for United, scoring 22 goals, after joining from Everton in 2013.
Fellaini wrote on Instagram: "Huge thank you to everyone I have worked with during my time Manchester United. I have made some great friends and wish them and the club every success for the future."
The Belgium midfielder, who last summer signed a new and improved deal until 2020, was a key figure at Old Trafford under Jose Mourinho.
But he has featured only once in United's seven Premier League games since the club sacked the Portuguese and appointed Ole Gunnar Solskjaer as caretaker manager, coming off the bench late in the first one, the 5-1 win at Cardiff on December 22.
Fellaini, who also under Solskjaer came on as a substitute in the 2-0 FA Cup third-round win over Reading on January 5, has been ruled out of recent matches by a calf injury.
United said in a statement on their website on Friday afternoon: "Manchester United can confirm that Marouane Fellaini has left the club on a permanent transfer.
"Everybody at United thanks Marouane for his service and wishes him well for the future as he completes his move to Shandong Luneng Taishan FC in China."
Fellaini had posted an Instagram photo of himself at an airport on Thursday morning, with the phrase "let's go" written across it.
He was the first major signing of United's post-Sir Alex Ferguson era when his former Everton manager David Moyes paid £27.5million for him in August 2013.
The divisive player went on to win the FA Cup in 2016 under Moyes' successor Louis van Gaal, and the League Cup and Europa League the following season under Mourinho.
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