Woodward revealed that as was in the case for fellow United star Robin van Persie, Louis van Gaal made the decision to part ways with Nani.
“The manager made the same decision regarding Nani as he did with Robin van Persie. As a club we also want to thank him for his services,” Woodward said.
Nani joined Fenerbahçe on a £4.3 million transfer from United last month and signed a three-year deal a week before Van Persie joined.
The Portuguese international won four Premier League titles, the Champions League and the World Club Cup during his time at Old Trafford.
The 28-year-old winger fell out of favour with former United manager David Moyes and his successor Van Gaal. Nani spent last season on loan at Portuguese giants Sporting Lisbon.
Nani made his debut for Fenerbahçe in the goalless draw against Shakhtar Donetsk in the Champions League preliminary play-off first-leg.
The experienced winger is expected to make his league debut against Eskişehirspor on the weekend.