Rooney has signed a two-year deal joined for an undisclosed fee believed to be £10m, according to The Sun. England and United's all-time record goalscorer will earn a reported £150,000-a-week and has become their highest earning player.
The deal is expected to be followed by confirmation of Romelu Lukaku's move to United for an initial £75m. A bid has been accepted by Everton for the Belgium international, who will undergo a medical before completing his switch to the 20-time English league champions.
"It is sometime since I said that the only Premier League club I would play for other than Manchester United was Everton, so I am delighted that the move has happened," said Rooney, in a statement to the Press Association.
"Thirteen years ago I went to United with the intention of winning trophies and I have been fortunate to be part of one of the most successful periods in the club's history.
"I have come back to Everton because I believe Ronald Koeman is building a team that can win something and I look forward to playing my part in making that a reality for the club I have support since a boy."
Manager Koeman said of Rooney, who joins the likes of Michael Keane and Jordan Pickford in moving to Everton this summer: "Wayne has shown me that ambition that we need and that winning mentality – he knows how to win titles and I'm really happy he's decided to come home. He loves Everton and he was desperate to come back. He is still only 31 and I don't have any doubts about his qualities. It's fantastic he's here."
During over a dozen years at United Rooney won 16 major honours and eclipsed Sir Bobby Charlton as their all-time record goalscorer. But in recent seasons, his importance has diminished and he made just 15 starts in the Premier League last term.
United boss Jose Mourinho added: "It is no secret that I have long been an admirer of Wayne; he has been a model professional throughout his time at the club and will remain in the history books for many years to come.
"It is never easy to see a great player playing less football than he would like and I could not stand in his way when he asked to go back to Everton. His experience, focus and determination will be missed and I wish him well for the future."