The news comes amid widespread criticism of the proposed European Super League, with United one of the six English clubs to have initially signed up to the project.
Woodward, who has been in the role since 2012, said: "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.
"The club is well positioned for the future and it will be difficult to walk away at the end of the year."
Woodward leaves Old Trafford amicably, with the club's co-owner, Joel Glazer, praising his work over the past nine years.
"On behalf of everyone at United I would like to place on record our sincere thanks for his tireless work and dedication," said Glazer.
"His contribution to the club has been massive, and he will always be welcome at Old Trafford as a part of the Manchester United family."
- updated April 21