The Exiles director of rugby, born in Australia, will work alongside defensive mastermind Mike Ford and forwards coach John Wells.
Johnson said: "The appointment of Brian is great news for England as we look forward to the increased time we have with the players under the new agreement with Premier Rugby.
"Brian is a top attack coach and I'm sure he will be a real asset to us. His appointment finalises the senior coaching team for next season."
Smith has been given the task of igniting England's pedestrian back play, which has proved woefully ineffective since 2003.
The recent tour to New Zealand once again exposed the shortcomings behind the scrum where the lack of imagination and creativity has made the team frustratingly one-dimensional.
Smith, a dual international for Australia and Ireland, is viewed as a visionary coach who has the ideas and drive to inspire the improvement required.
His track record at London Irish, who he guided to the European Cup semi-finals last season, is superb.
The Exiles are one of the Premiership's most entertaining sides and it is hoped Smith will be able to translate his attacking philosophy from club to Test level.
Smith said: "The opportunity to coach Test rugby comes along rarely in one's career so I'm looking forward to my new position with England.
"It's an exciting time to be involved. I would like to thank London Irish for the opportunity the club has given me.
"I've enjoyed working with the playing and coaching staff and would like to thank all at the club for all the encouragement I've received."
Northampton's highly-rated director of rugby Jim Mallinder was viewed as a rival for the job but cleared Smith's path to Twickenham by committing his future to Saints.
Johnson, the England manager, placed Smith at the top of his wanted list some time ago but had to wait for the Rugby Football Union to complete talks with Irish.
Exiles director John Conlan said: "We're pleased negotiations for the release of Brian Smith from his contract have been conducted in a good natured way and concluded to the satisfaction of both parties.
"On behalf of all at London Irish I would like to thank Brian for his contribution to the club over the past three seasons.
"It has been an era of significant progress that we are determined to build on."
Smith arrived at the Madejski Stadium in 2005, guiding the club to third place in the Premiership and a European Challenge Cup final during his first season in charge.
But those achievements were surpassed last season when Irish stormed into the last four of the European Cup where they were edged by Toulouse.