Record-breaking teen Shaw joins Man Utd
England full-back Luke Shaw (top) in action during a Group D match against Costa Rica at the Mineirao Stadium in Belo Horizonte during the 2014 FIFA World Cup on June 24, 2014 - by Ronaldo Schemidt
The fee for the 18-year-old, who has just returned from England's worst-ever World Cup campaign, surpassed the £25.6m fee United paid Everton for Wayne Rooney in 2004.
"Manchester United is delighted to announce the signing of Luke Shaw from Southampton Football Club," a United statement said.
While both clubs refused to confirm the exact transfer fee, a statement on Southampton's website said Shaw had become "the most expensive teenager ever".
His arrival at Old Trafford meant United had taken their spending on new players to an estimated £60m in two days as they rebuild after a dire 2013/14 season.
Thursday saw United complete their first signing since Louis van Gaal, currently coaching the Netherlands at the World Cup, became their manager after midfielder Ander Herrera joined from Athletic Bilbao for a reported £28.5m.
"I am thrilled and excited to be joining Manchester United," Shaw told his new club's website after passing a medical.
While thanking Southampton, the south coast club he had been with since the age of eight and for whom he made 67 senior appearances since his professional debut in 2012, Shaw said he'd no hesitation in joining United.
"I want to continue to progress my career and joining United is the ideal place for me to do that," he said.
"I am looking forward to this new chapter in my life and also looking forward to learning from the world-class players and management at the club."
Game has become 'silly' says Scholes
Shaw won the third of his three England caps in the goalless draw with Costa Rica that saw Roy Hodgson's men, already eliminated following defeats by Italy and Uruguay, conclude their wretched World Cup.
"Luke is a very talented young left-back with great potential" said United assistant manager Ryan Giggs.
"He has developed immensely during his time at Southampton and has all the attributes to become a top player."
But Giggs's former United team-mate Paul Scholes said the transfer was an example of "something which has a bad long-term impact" for English football.
Writing in a blog for bookmakers Paddy Power, before the deal was confirmed, ex-England midfielder Scholes said: "(English) Clubs are priced out of this market which is why they go abroad for cheap options.
"For a left-back to be worth £34m shows how silly the game has gone."
Shaw was a key figure in a promising Southampton side who finished eighth to United's seventh in last season's Premier League table.
But that team appears to be unravelling.
England striker Rickie Lambert has already left for Liverpool, with midfielder Adam Lallana, his club and international team-mate, poised to do likewise.
However, Southampton promised the money from Shaw's move would be reinvested in a team now managed by former Dutch international Ronald Koeman, after former boss Mauricio Pochettino left to join fellow Premier League side Tottenham Hotspur.
"The fee will amount to the highest-ever transfer fee received by the club, making the 18 year-old the most expensive teenager ever," Southampton said.
Saints executive director Les Reed, in what appeared to be a message to Liverpool regarding Lallana, told the club's website: "This deal is a good one for Southampton Football Club, and hopefully sends a clear message to other clubs wishing to bid for our players.
"Luke’s transfer fee will be reinvested into the team as our new manager, Ronald Koeman, builds for the new season and for years to come.”
United started last season as champions of England but their failure to qualify for the Champions League led the club to sack David Moyes -- retired United manager Alex Ferguson's chosen successor at Old Trafford -- and install Giggs as caretaker boss before appointing the experienced van Gaal.