The 31-year-old arrived in Istanbul over the weekend and will take part in a signing ceremony at the club's stadium at 6pm local time (4pm GMT) where he is expected to finalise his transfer from United.
Ahead of that ceremony, the club posted on their Twitter account: "Welcome to #Fenerbahce! @Persie_Official"
Van Persie will depart Old Trafford after scoring 58 goals over three years, with 30 of those coming during his maiden campaign in 2012-13 when he fired United to an unprecedented 20th top-flight title in Sir Alex Ferguson's last season in charge.
He was the Barclays Premier League's leading marksman in back-to-back seasons between 2011 and 2013, swapping Arsenal for United in-between in a Â£24million move.
The Dutchman was seen as the missing piece for United when he joined in 2012 and his goal-laden first term at Old Trafford helped provide Ferguson with a fitting send-off.
However, Van Persie's role gradually diminished under first David Moyes and then his old Holland manager Louis van Gaal as a series of niggling injuries hampered him.
And, having signed Matteo Darmian, Bastian Schweinsteiger and Morgan Schneiderlin in recent days, Van Gaal has continued to shake up his squad by offloading the man who was his captain when he took Holland to the World Cup semi-finals last summer.
Van Persie will link up with his former United team-mate Nani, who joined Fenerbahce earlier this summer, in Turkey while Raul Meireles is also in the Istanbul club's ranks.
Source : PA