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The news comes amid chaos around the planned European Super League, in which United are set to take part.
Woodward, 49, joined the Old Trafford club in 2013 and played a key role in The Super League.
His exit is understood to be amicable with the owners and is said to be unrelated to the Super League despite the striking timing.
“I am extremely proud to have served United and it has been an honour to work for the world’s greatest football club for the past 16 years,” Woodward said in a statement. “The club is well positioned for the future and it will be difficult to walk away at the end of the year.
“I will treasure the memories from my time at Old Trafford, during a period when we won the Europa League, the FA Cup and the EFL Cup. I am proud of the regeneration of the club’s culture and our return to the Manchester United way of playing.”
He added: “I would like to thank United’s passionate fans for their support during the good and bad times. I know this has been a challenging period in our history, but your support for the team has never, ever been in doubt.
“Finally, it has been a pleasure to work with so many magnificent, talented and hard-working people.”
Former United defender Gary Neville, who this week called for United’s owners, the Glazer family, to sell the club, appeared to celebrate Woodward’s exit.
The right-back, who has spoken out passionately against The Super League since Sunday, tweeted a waving hand emoji after news emerged of Woodward’s resignation.
The Independent understands Chelsea are preparing to withdraw from the breakaway competition with Manchester City already confirming their exit.
Plans for the tournament involved 12 of the biggest clubs in Europe, including United, City, Chelsea, Liverpool, Tottenham and Arsenal, with Real Madrid, Atletico Madrid, Barcelona, Juventus, AC Milan and Inter Milan also joining.
The proposals, which emerged on Sunday, were immediately met with widespread condemnation from fans, players and clubs around the world, putting immense pressure on the Super League participants.
Additional reporting by PA