The 42-year-old was interim boss for the Six Nations, after Martin Johnson resigned, and led England to second place with four wins from five matches.
“I am immensely honoured and proud to accept this role,” said Lancaster, who was interviewed for the job, along with former South Africa coach Nick Mallett.
Lancaster’s first major task as permament head coach will be picking a squad for the three-Test tour of South Africa in June.
Later this year England play Fiji, Australia, South Africa and New Zealand on consecutive weekends in their autumn programme.
“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,” said Lancaster.
Forwards coach Graham Rowntree is expected to remain part of Lancaster’s team but he faces a battle to retain Andy Farrell, who acted as backs and defence coach during the Six Nations.
Saracens are reluctant to release Farrell from his job as first-team coach at the club.
Lancaster was the number one choice with players, with back-row forward Phil Dowson saying the whole squad would back him.
“We spoke to him at the end [of the Six Nations] and I think he was absolutely exhausted because he left no stone unturned in terms of creating an environment and an atmosphere that was akin to a club,” said Dowson.
A former director of rugby at Leeds, Lancaster was in charge of England’s Saxons second team and elite player development at the RFU before taking over the national team.
As temporary boss, the former school teacher helped restore morale and reputation following England’s dismal World Cup campaign, which saw a quarter-final exit and was marred by off-field controversies.
After news of his permanent appointment broke, England and London Irish prop Alex Corbisiero said on Twitter: “Right decision has been made.”
Ian Ritchie, the RFU’s new chief executive, oversaw the recruitment process and said Lancaster had “the skills and vision” needed to be a success.
He was assisted by an advisory panel comprising Conor O’Shea and Ian McGeechan – the Harlequins and Bath directors of rugby respectively – the RFU’s professional rugby director Rob Andrew and former England flanker Richard Hill.
“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,” said Ritchie.
Lancaster’s period as interim coach included a victory over World Cup finalists France in Paris and a 30-9 defeat of Ireland at Twickenham.
Former England coach Dick Best told BBC Radio 5 live that Lancaster deserved the job, but faced a difficult start.
“He has done remarkably well in a short space of time. The honeymoon period is now over. It’s a fairly tough beginning for his full-time role,” he said.
“They are on course but they have to go up a couple of notches from the Six Nations for the games in South Africa and the autumn.”