He has, however, offered to continue to lead the Test side on an interim basis for the upcoming series against England and Australia "if this is considered helpful for the new captain".
"I would like to announce that after careful consideration I have concluded that it is in the best long-term interests of the team that I step down now as national captain so that a new leader can be properly groomed for the 2015 World Cup in Australia," a statement from Sangakkara said.
"This was a decision I made prior to the 2011 World Cup.
I will be 37 by the next World Cup and I cannot therefore be sure of my place in the team. It is better that Sri Lanka is now led by a player who will be at the peak of his career during that tournament."
Thilan Samaraweera is likely to be named Sangakkara`s successor for the Test side, while Tillakaratne Dilshan and Angelo Mathews are discussed as options to take charge of the ODI and T20 sides.
The 33-year-old left-hander, however, is keen to continue playing in all formats of the game for the next few years.
"I have no plans of retirement from international cricket at this stage and subject to form and fitness I would like to be considered for selection in all three formats of the game for the foreseeable future."
Sangakkara, who scored 48 in the title clash of the World Cup, finished the tournament with 465 runs at an average of 93.
"It has been a true honour and a great privilege to serve my country as captain during the past two years and, although bitterly disappointed that we could not win the final, I am very proud of the performances of the team.
"I met with the selectors on Monday and I explained my reasons for my decision and I assured them of my fullest support in helping our new captain settle into the leadership.
"In this regard, I have offered to continue as the Test captain for the forthcoming series with England and possibly Australia if the selectors believe this would help the new captain and aid the transition.