France midfielder Paul Pogba said he felt it was his destiny to return to Manchester United after he completed his move from Juventus on Tuesday for a world-record 105 million euros (116 million dollars).
The amount will be paid over two financial years, and may increase by 5 million euros should "given conditions" be achieved during the contract, a statement on the club's website said.
The previous biggest transfer was Gareth Bale's move to Real Madrid from Tottenham in 2013 for allegedly 100 million euros.
United confirmed Tuesday that Pogba is to receive a five-year contract at the club until 2021, with the option for another season and Pogba said it felt like he had come home.
"It was like I just went for a holiday," he told MUTV, the club's internal television station. "I've come back home.
"I think it's destiny. At first my mum told me I would come back here and I told her, 'you never know, we will see'.
"For myself it was a big challenge for me to come back to where I started. I didn't finish what I started here so I think I came to finish it."
The 23-year-old is considered one of the hottest properties in European football. The 36-times capped France midfielder joined the United youth teams as a teenager in 2009 and left for Juve in 2012.
"I only think about the pitch. I want to do great, I want to be one of the best, I want to win titles, I want to achieve things," he said.
"That's why I came here - to do this, to become one of the best. I want to win titles because I know this club has to win titles.
"This club is great to win titles with, to win big things. I'm focused on this and I'm just ready to go... and just kill it."
In a statement on United's website, Pogba said he was looking forward to working under new United manager Jose Mourinho.
"I have thoroughly enjoyed my time at Juventus and have some fantastic memories of a great club with players that I count as friends," he said.
"But I feel the time is right to go back to Old Trafford. I always enjoyed playing in front of the fans and can't wait to make my contribution to the team. This is the right club for me to achieve everything I hope to in the game."
Pogba is United's fourth signing of the summer under new manager Jose Mourinho, joining Zlatan Ibrahimovic, Eric Bailly and Henrikh Mkhitaryan.
"Paul is one of the best players in the world and will be a key part of the United team I want to build here for the future," Mourinho said.
"He is quick, strong, scores goals and reads the game better than many players much older than he is. At 23, he has the chance to make that position his own here over many years," he added.
"He is young and will continue to improve; he has the chance to be at the heart of this club for the next decade and beyond."
Mourinho says he plans to take United back to the top of the Premier League. United won the FA Cup under predecessor Louis van Gaal, and under Mourinho on the weekend beat Premier League champions Leicester in the Community Shield.