The former home secretary, foreign secretary and lord chancellor broke the news to his constituency Labour Party in Blackburn, the Lancashire town which he has served as MP since 1979.
Mr Straw, 67, said it would be a "terrible wrench" to leave the House of Commons at the election, scheduled for May 2015, but that he did not want to push his luck by attempting to stay on into his 70s.
Labour leader Ed Miliband paid tribute to the "eloquence and wisdom" of a politician who has sat in the Commons for 34 years.
He appeared to hint at the possibility of a seat in the House of Lords for Mr Straw, who he said "will continue to serve our country in many different ways".
And Mr Straw made clear his support for Mr Miliband, saying he had "the ability, the determination and the character to take this country to a better and much fairer place than under this Government".
He promised to devote all of his energies" to putting Mr Miliband into 10 Downing Street and said he had no doubt that Labour could win under his leadership in 2015.
Mr Straw told constituency activists that he had made the decision to stand down after a great deal of thought and consultation with friends and family, including wife Alice.
"Labour is part of my soul, and so is this town," he told them."Luck does play a significant part in anyone's fortunes, and, as I have said, I have been very lucky. So, to put this another way, I did not want to push my luck, to tempt providence."