Straw cited his age when he announced his decision, the Daily Mirror reported. He will be 69 in 2015.
"I can't go on forever," he said.
Straw has represented Blackburn in Lancashire as a Labor member of Parliament since 1979. He spent 17 years as a minister and was one of three people to be in the cabinet continuously from Labor's overwhelming victory in 1997 to its defeat in 2010.
Under Prime Minister Tony Blair, Straw was home secretary from 1997 to 2001 and was then named foreign secretary. He became controversial because of the Blair government's support of U.S. President George W. Bush during the invasion of Iraq.
Straw was moved to House of Commons leader during a major reshuffle in 2006.
In a statement, Straw said he is confident Labor under Ed Miliband, its current leader, will win in 2015. He promised to work hard to make sure the party retains the Blackburn seat.
Blair called Straw "a true Labor giant," the Lancashire Telegraph reported.
"Jack's contribution to law and order in Britain and this country's standing in the world is quite simply formidable," Blair said. "In 2015, Parliament will lose one of the most able politicians of my generation, but I have no doubt that he will be immensely successful in whatever he turns his hand to next."