Belgium international Fellaini has agreed a three-year contract worth around £12.2 million a year to move to Shandong, with United expected to receive around £10.5m for the 31-year-old.
Fellaini signed a new two-year deal at Old Trafford in the summer, but has found opportunities limited under caretaker manager Ole Gunnar Solskjaer.
He has passed a medical at Shandong, who are third in the CSL, despite missing United's last four games with a calf injury.
It means Fellaini's five-and-a-half year stay at United will come to an end after 177 appearances and 22 goals.
He arrived in a £27.5 million deal from Everton as David Moyes' first signing and won the FA Cup, League Cup and Europa League at Old Trafford.
Meanwhile, United have announced that Matty Willock has joined Crawley Town on loan for the rest of the season.
The 22-year-old midfielder spent the first half of the season on loan at St Mirren.