The Rugby Football Union management board unanimously approved Johnson's appointment following a meeting at Twickenham on Wednesday.
Brian Ashton ceases to be England head coach, and has been offered a role as head coach of the RFU's national academy.
There is no news at this stage whether or not 61-year-old Ashton, who took charge of England for 22 Tests and led them to last autumn's World Cup final, will accept Twickenham's offer.
The RFU say 38-year-old Johnson will report to their elite rugby director Rob Andrew, and will have "full managerial control" of the England team.
Andrew, meanwhile, is to be England's team manager for the Barbarians clash at Twickenham on June 1, and the two-Test tour of New Zealand later that month.
Existing forwards coach John Wells and defence coach Mike Ford - Ashton's lieutenants this season - are to remain in their posts.
The coaching team for England's two-Test New Zealand trip has been confirmed as Wells, Ford, Graham Rowntree and Jon Callard.
Johnson said: "It is a great honour for me to be offered this position.
"I am passionate about the England team and delivering success for it.
"While I cannot take up my position until July 1 for personal reasons (Johnson's wife Kay is pregnant) I will be working closely with Rob and the England coaching team on selection for the Barbarians match and the New Zealand tour, as well as selecting the first senior elite player squad of 32 under the new agreement between the RFU and Premier Rugby."
It has also been confirmed Johnson will appoint an additional coach to his team.
That is likely to be a backs specialist - Ashton's area of expertise - with Johnson's 2003 World Cup colleague Mike Catt among those whose name has already been linked.
Andrew added: "I am delighted Martin is joining the England structure as team manager.
"He will bring a new and fresh approach to team development and preparation in his own inimitable style.
"I would also like to thank Brian for the job he has done in difficult circumstances.
"He is an outstanding coach and deserves enormous credit for leading England to a second successive Rugby World Cup final last year and securing the runners-up position in this year's RBS 6 Nations.
"While Brian is naturally disappointed that he will not have a role in the new senior structure, I believe the new post that we have offered him as head coach of the national academy is ideally suited to his special talents and expertise."
RFU chief executive Francis Baron said: "Martin has the freedom and the budget to recruit additional coaching resources and make other changes to the England set-up to build a team that will consistently challenge for the major international tournaments.
"I am also personally pleased that Brian has been offered a senior post within the RFU which I very much hope he accepts. He still has much to offer England rugby."
The job offered to Ashton would encompass working across the England Saxons, England Under-20 and England Under-18 groups.
During his reign as head coach, England reached a second successive World Cup final and were runners-up in this season's RBS 6 Nations.