He told reporters that his deputy, Najib Razak, would become leader of the governing Umno party in June 2010.
The prime minister has been under intense pressure to resign over poor election results and high fuel prices.
The move comes amid allegations against Mr Najib of a sex scandal involving a Mongolian woman who was found murdered. Mr Najib denies any link to the woman.
Traditionally, the party leader becomes the prime minister.
Mr Abdullah, whose mandate expires in mid-2013, announced his decision at a news conference.
He said he had agreed with Mr Najib to hand over power but that he first wanted the opportunity to implement reforms initiated since he took office in 2003.
"There are many things and programmes I want to achieve before I hand over and I hope that Najib will continue as my deputy in carrying this out," he said, flanked by Mr Najib and Umno officials.
He said he was confident that Mr Najib would "lead the party well"
Source Malaysia's Abdullah to stand down BBC News, UK - 13 minutes ago