Sir Jim Ratcliffe (left) has made frequent visits to Old Trafford and the club's training ground since his deal was agreed
The British billionaire's investment is worth about $1.6bn (£1.25bn).
The Glazer family, who have owned the 20-time English champions since 2005, will retain a majority stake in the club but Ratcliffe's Ineos Group will take control of football operations.
"To become co-owner of Manchester United is a great honour and comes with great responsibility," said Ratcliffe.
"This marks the completion of the transaction, but just the beginning of our journey to take Manchester United back to the top of English, European and world football, with world-class facilities for our fans.
"Work to achieve those objectives will accelerate from today."
Manchester-born Ratcliffe is chairman of petrochemicals company Ineos and says he is a lifelong supporter of United. He tried and failed to buy Chelsea in May 2022.
The 71-year-old businessman has agreed to buy 25% of United's class B shares, largely held by the Glazer family, which contain almost all the voting rights, and up to 25% of its class A shares, which are listed on the New York Stock Exchange.
The deal, which was agreed on Christmas Eve, also includes $300m (£237m) for future investment in the club's Old Trafford stadium. The initial $200m (£158m) of that commitment elevates Ratcliffe's shareholding to the 27.7% mark, with the remaining $100m ($79m) to follow by the end of the year.
Taking on sporting control at the club means Ineos will oversee the men's and women's football operations and academies.
They will also get two seats on the Manchester United plc and Manchester United Football Club boards.
Ratcliffe made several visits to Old Trafford and the club's training ground while he waited for the deal to receive final approval.
His investment had already been approved by the Football Association and Premier League, with Ratcliffe having signed the top flight's owners' charter.
The deal is the first to be agreed under the Premier League's updated owners' and directors' test, which was approved by member clubs in March 2023 and includes a review by an independent oversight panel.
The Glazers bought Manchester United for £790m in 2005. In November 2022, the American family stated they were considering selling in order to "explore strategic alternatives".
-- Courtesy of BBC Sport