The 35-year-old Strauss, who will be replaced as test captain by fellow opening batsman Alastair Cook, blamed a dip in form with the bat as the primary reason for his "difficult decision."
"I haven't batted well for a long time now," said Strauss, who made 100 test appearances for England — 50 as captain. "I knew with my own energy levels and motivation that I wasn't going to improve, batting-wise. I'd run my race.
"It's a hugely sad moment in many ways."
Having risen to No. 1 in the test rankings with a series whitewash of India last year, England relinquished that status this month by losing a home series to South Africa.
That series was marred by the axing of Kevin Pietersen from the squad for sending "provocative" texts to South African players about Strauss.
Strauss, however, denied the controversy involving Pietersen was a factor in his decision.
"Not in anyway," said Strauss, speaking at a hastily convened news conference at Lord's — the home ground of his county team Middlesex. "I've been speaking about it for a while. I first spoke to (England coach) Andy Flower about it prior to the Kevin Pietersen incident rearing its head, it just hasn't been a consideration at all.
"What happened I didn't feel undermined me in the eyes of the team. It was obviously a difficult situation to deal with, but not in terms of making me more or less keen to lead the side forward."
Mirroring the attitude that marked his tenure as captain, which began in 2009 when he succeeded Pietersen, Strauss spoke with composure and authority at the end of a draining summer that was uncomfortable for him on and away from the crease.
He reflected on a test career that finished with a batting average of 40.91, 21 centuries — his first coming on his debut against New Zealand at Lord's in 2004 — and 27 half-centuries with pride. The highlight of his international career, he said, was undoubtedly the 3-1 test series win in Australia in 2010-11 which saw England retain the Ashes in the back yard of its fiercest rival.
That was one of the results that helped him become the second most successful test captain in terms of results, behind Michael Vaughan.
"His legacy within the game will be felt for many years to come and we now need to continue to build on the progress we have made under his leadership," said David Collier, chief executive of the England and Wales Cricket Board.
Cook said it was a "sad dressing room" when Strauss notified the team of his decision on Tuesday.
"He has been a fantastic captain, has led from the front for three-and-a-half years and is a true ambassador for the game," said Cook, who flanked Strauss at the news conference.
"To have played 100 tests for your country is a phenomenal achievement and I want to congratulate him on a superb career."
Cook, who has played 83 tests for England and took over as one-day captain last year, will take charge of the test team for the first time in the away series against India later this year.
"It's time for the side to refresh and think about how to regain that No. 1 ranking," Strauss said. "Alastair will come in and give the side a huge amount of energy.
"I think for a captain to perform his role properly, it's important you're not a passenger in the side, but also that people aren't speculating as to whether you should be in the side or not. I think that would have been too big a distraction to the side going forward."
Strauss, who began his first-class career with Middlesex in 1998 and was an unfussy, compact strokemaker, made his bow in international cricket in 2003 when he made the first of 127 one-day appearances. He also played in four Twenty20 internationals.
"I'd love to stay involved in the game," Strauss said. "I'm hugely passionate about the game. I feel like I've got more to offer the game at some stage in the future. But in what capacity, I've got no idea."