Mr Bouteflika, who had been in power for 20 years, had already dropped plans to seek a fifth term as opposition to his rule grew.
The powerful Algerian army had called for the 82-year-old to be declared incapable of carrying out his duties. The ailing leader suffered a stroke six years ago and has rarely appeared in public since.
State TV reported that he had officially notified the Constitutional Council that he would end his term as president from Tuesday.
The BBC quoted the APS news agency to have reported that the Military head Lt Gen Ahmed Gaed Salah said: “There is no more room to waste time.” Leaders of the protests had rejected Mr Bouteflika’s offer to go by the end of his current term – 28 April – as not enough. The demonstrations have also led to calls for the whole political system, in which the military plays a significant role, to be overhauled. Many of the protesters are young and say they want a new system of government. There have been accusations that Mr Bouteflika is being used as a front by “le pouvoir” – a group of businessmen, politicians and military officials – to retain their power.
The governing National Liberation Front (FLN), which postponed elections originally scheduled for 18 April, had vowed to organise a national conference on reforms.
The FLN has ruled Algeria since the country won independence from France in 1962 after seven years of conflict.
Mr Bouteflika, who came to power in 1999, strengthened his grip after a bloody civil war against Islamist insurgents which left 150,000 dead.
Reports say car horns could be heard in the streets of the capital, Algiers, following the announcement that Mr Bouteflika had submitted his resignation.
The chairman of the upper house of parliament, Abdelkader Bensalah, is expected to become caretaker president for three months until elections.