The ailing 82-year-old who has been confined to a wheelchair has been seeking medical treatment abroad until his return to the country on Sunday.
“There was never any question of it for me. Given my state of health and age, my last duty towards the Algerian people was always contributing to the foundation of a new Republic” Bouteflika was quoted as saying.
The statement also announced that the presidential election which was slated for 18 April has been indefinitely postponed.
Bouteflika was in the running for a fifth term as Algeria’s president until Monday’s announcement which was met with scenes of wild celebrations in the streets of the capital Algiers.
His controversial attempt to bid for another term had provoked widespread anger in Algeria and set off weeks of demonstrations calling on him not to stand.
However, there are question marks over whether he will resign before or after the next presidential election.
Bouteflika has led Algeria since 1999.
However since his fourth term the Algerian leader has been confined to a wheelchair after suffering a stroke in 2013.
Since then he has made rare public appearances.
A new date will be announced for the presidential election.
In a major development Prime Minister Ahmed Ouyahia has resigned and handed over the role to his successor Interior Minister Noureddine Bedoui.
The new PM is expected to form a new government over the next few days.