Rooney, 31, played 559 times for United, scoring 253 goals.
He won five Premier League titles and each of the Champions League, Europa League and FA Cup once after joining from Everton for £27m in 2004.
Rooney, who has signed a two-year deal, said he was “ecstatic” and his “first game back will be an emotional day”.
“It’s a great feeling to be back. I cannot wait to meet the lads, get on the training pitch and then get on the pitch to play,” he added.
Rooney’s return comes as United look set to sign Everton striker Romelu Lukaku, with a £75m deal for the Belgium international agreed between the two clubs.
Everton confirmed Rooney will wear the number 10 shirt previously worn by Lukaku.
“I’m not just coming back because it’s the team I support, the team I grew up playing for – I’m coming back because I feel the club can move forward and be successful,” said Rooney, who scored 17 goals in 77 games in his first spell at Goodison.
“I want to be part of it. There will be pressure on me to perform, but I’m ready to go. I believe I can help move this club forward and be more successful on the pitch.”
Rooney says when he spoke to Everton manager Ronald Koeman, he “saw it in his eyes that he wanted me to be part of his team”.
He added: “It was a no-brainer for me and the only place I was going to go.”
Rooney said he told his agent Paul Stretford to “go and speak to them, let’s make it happen” when he found out Everton were interested in signing him and it “was obvious I was going to be leaving Manchester United this summer”.
“There were other options there but once I knew that Everton wanted me to come back then it was the only option for me,” he added.
Why Everton want him back
Koeman began talking about Rooney’s potential return as far back as October, stating he would be “pleased” to sign England’s all-time leading goalscorer.
On Sunday, he said: “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.
“We have a lot of young players and sometimes in life you need somebody who you look up to, who you learn from. That was also one of the messages when we spoke about on and off the pitch what his function will be in the team.
“One of the functions for Wayne is to show the rest of the team why he is – and still is – that player.”
Rooney, who was often left out of United’s starting line-up by manager Jose Mourinho last season, appeared in 25 league games – the fewest he has played in one season. His total of eight goals in all competitions was also the lowest of his career.
He also lost his place in the England squad, but has not retired from international duty and needs six more caps to equal goalkeeper Peter Shilton’s all-time record of 125 appearances.
Rooney was an unused substitute as United beat Southampton to win the EFL Cup in February, and made only a brief appearance at the end of the Europa League final victory over Ajax in May.
In his 13 seasons with United, he finished as top scorer five times and shared the honour with Cristiano Ronaldo in another campaign. He was also named fans’ player of the year twice.
“It is no secret that I have long been an admirer of Wayne,” said Mourinho. “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.”
Executive vice-chairman Ed Woodward added: “Who can forget his storybook debut hat-trick against Fenerbahce, the spectacular overhead kick against Manchester City and the countless match-winning performances in his time here?