The 50-year-old will vacate the top operational role in the Red Devils boardroom from February 1 after 16 years at the club.
Arnold will step up to effectively fill Woodward's position, becoming Man United's first chief executive since David Gill stepped down from that role in 2013.
Arnold was previously the club's group managing director, and commercial director before that, having joined the club in 2007 following a role as an executive a Nasdaq-listed technology company InterVoice.
A statement from the Premier League giants read: "Manchester United has announced that Richard Arnold, formerly Group Managing Director, will become Chief Executive Officer of the Club, effective from 1st February 2022.
"Ed Woodward will step down from his role as Executive Vice-Chairman, also effective from 1st February 2022."
New chief exec Arnold said: "I am honoured to have the chance to serve this great club and its fans. I am determined to return that honour in any way I can."
Woodward announced he'd be leaving his role at the end of the year in April 2021 in the midst of the fallout from the European Super League but his departure was delayed following the exit of Ole Gunnar Solskjaer as manager and appointment of Ralf Rangnick as interim boss.
"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," he said at the time.
"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.
"We have invested more than £1billion in the squad during my time here and I am particularly delighted with the progress the players have made under the astute leadership of Ole Gunnar Solskjaer and his coaching team in the last two years.
"I am sure that with the changes we have made on-field and to the coaching and football staff in recent years this great club will soon be lifting silverware again. It deserves to.
"I desperately wanted the club to win the Premier League during my tenure and I am certain that the foundations are in place for us to win it back for our passionate fans."
Woodward's association with the Red Devils began in 2005 when he acted as an adviser to help the Glazers buy the club.
He was originally handed the reins of United's commercial and media activities in 2007, but grew more and more influential after increasing the club's global value dramatically.
Appointed executive vice-chairman in 2012, he oversaw numerous big-name signings.
But he drew criticism from managers and fans alike for a perceived failure to improve the squad during the post-Sir Alex Ferguson era.
The Red Devils have failed to win the title since Woodward assumed all responsibilities for football operations from David Gill in 2013, although they have managed to lift the FA Cup, League Cup and Europa League in the last nine years.
Former United boss Louis van Gaal expressed concerns about Woodward's commercial activities hindering the club, while Jose Mourinho publicly accused the him of vetoing his transfer list when he was United manager in 2018.
In January 2020, Woodward's Cheshire home was attacked by a group of disgruntled supporters, who chanted that he was 'going to die'.
Before Old Trafford's doors were shut due to the pandemic in March 2020, chants calling for Woodward and the Glazers to go were common during United's home games.
Solskjaer's sacking in November 2021 was the fourth manager to be dismissed during Woodward's time in the role, after Moyes, Van Gaal and Mourinho's departures.
Rangnick has since been handed the reigns at Old Trafford in an interim role and the club has overseen a tricky start in charge.
He's overseen three victories in six outings since stepping in the dugout but the performances have been less than convincing.
Whether the German will be handed the permanent role remains to be seen, but if he isn't he will step into the club's hierarchy in a consultancy role.