Sir Jim Ratcliffe, the British billionaire owner of INEOS, is acquiring 27.7% of the club.
Ratcliffe has bought class A and class B shares to ensure he has the appropriate holding in the Red Devils.
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On the announcement, Ratcliffe said: "To become co-owner of Manchester United is a great honor and comes with great responsibility.
"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."
Chairman Joel Glazer, whose family are still majority shareholders, added: 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."