The 42-year-old, who led England to four wins out of five in this year's Six Nations championship, has been chosen ahead of former South Africa and Italy coach Nick Mallett.
"We have been through a rigorous and global selection process and are confident that Stuart is the right person to lead England Rugby forward into the 2015 Rugby World Cup," RFU chief executive Ian Ritchie said.
"He has shown throughout the RBS Six Nations and subsequently in both interview and other conversations I, as chairman of the advisory panel, have had with him that he has the skills and vision needed in the England head coach."
Lancaster said: "I am immensely honoured and proud to accept this role.
"We have a massive task ahead of us in South Africa this summer and we have 37 games before that first World Cup match on home soil, so every second counts in developing players who can win that tournament - which has to be the ultimate aim."
The coaching appointment was the first big decision for new CEO Ritchie, whose choice had to be rubber-stamped by the RFU council.
Lancaster was appointed interim coach for the Six Nations after Martin Johnson stepped down in November following England's poor World Cup campaign in New Zealand.
He had previously led England's second-string Saxons team and was working for the RFU as head of elite development.
Those positions gave him in-depth knowledge of the up-and-coming players available to England and he took full advantage by handing out seven new caps in his first game in charge, away to Scotland.
England won that match, their first in Edinburgh in four attempts, and followed up with another win in Rome.
Lancaster's first outing at Twickenham ended in a last-gasp defeat to eventual Grand Slam champions Wales but he finished impressively with victory in France and then a 30-9 home thumping of Ireland.
The four wins put England second in the standings, a step down from last year's title but an unexpectedly impressive showing on the back of their flat World Cup displays.
England's fans embraced Lancaster's willingness to throw in new faces and were equally impressed by the way he turned the team's attitude around following the stream of negative headlines during the World Cup.
From the day he took charge Lancaster made it his stated aim to "restore the pride in wearing the England shirt" and ensure the players reconnected with the grass roots game.
He took them for a week's training camp at a junior club in Leeds and brought in motivational speakers from other sports.
Scrum coach Graham Rowntree, the only survivor from the World Cup coaching team, said last week that Lancaster had "dragged England out of the gutter" and that the Six Nations campaign had been the "perfect interview".
Lancaster took on the more formal interview this week where he laid out his blueprint to have developed the current crop of fledgling players into an experienced 600-cap group perfectly placed to make an assault on the next World Cup which they host in 2015.