"To become co-owner of Manchester United is a great honour and comes with great responsibility," Ratcliffe said in a statement on Tuesday.
"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."
The ownership deal still faced hurdles, including Premier League approval which was given last week.
The Glazer family have owned United since 2005 and will retain a majority stake in the club but Ratcliffe's Ineos Group will take control of football operations.
"I would like to welcome Sir Jim as co-owner and look forward to working closely with him and INEOS Sport to deliver a bright future for Manchester United," executive co-chairman Joel Glazer said in a statement.
Ratcliffe has agreed to purchase 25% of the team'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 71-year-old Ratcliffe, who grew up a United fan, told reporters recently that ownership in the club is the most exciting endeavour of his life.
The 20-time English champions are sixth in the league.
