It's unclear if the stunning move will appease the masses of protesters whose vociferous calls for Bouteflika and his cadre of loyalists to quit have expanded to demand an overhaul of the entire political system.
Their weekly protests since Feb. 22 have challenged the political status quo in the country long ruled by Bouteflika, 82, a onetime wily political survivor who has rarely been seen in public since he suffered a stroke in 2013.
A short statement from Bouteflika's office said he would take "important steps to ensure the continuity of the functioning of state institutions" after he leaves the office he assumed in 1999. The Algerian Constitution calls for the head of the upper house of parliament, Abdelkader Bensalah, to act as interim leader for a maximum of 90 days while an election is organized.
Algerian national television reported Sunday night that Bouteflika and the replacement prime minister he appointed last month, Noureddine Bedoui, had formed a new government after struggling for weeks to find potential Cabinet ministers amid the uncertainty surrounding the president.
The new government must stay in place during the transition period before the next election. In recent weeks, the president saw key figures withdraw their support from him. Algeria's powerful army chief proposed launching a procedure to have Bouteflika declared unfit for office, prompting tensions between the army and the president's inner circle.
The president's concession came after a court in Algeria said it was investigating corruption and the illegal transfer of funds abroad amid concerns about a flight of capital from the country amid political instability.
The official APS news agency quoted the Algerian prosecutor's office Monday as saying "certain people" were banned from leaving the country "for the needs of the investigation," providing no details. Police detained a powerful industrialist who is thought to be close to Bouteflika, Ali Haddad, near the Algerian-Tunisian border over the weekend.
Algeria is Africa's biggest country by land mass and a major natural gas producer, but its energy riches have not trickled down to reach the pockets of its people. The protests have been driven mostly by young Algerians, many of whom struggle to find jobs. Desperation has driven some to attempt to migrate to Europe on rickety boats.
Demonstrators said Bouteflika and the rest of the political establishment were out of touch with their everyday problems. They have called for a rewritten constitution that gives fewer powers to the president in a bid to strengthen democracy in the gas-rich North African country.
Ending his presidency amid the protests was a bold decision for Bouteflika, who in February declared he would seek a fifth term in the presidential election originally scheduled for April 18. He postponed the election and said he would not be a candidate when it was held, but did not set a new date, angering critics who saw the delay as designed to hold onto power.
Bouteflika had been known as a political survivor ever since he fought during the 1950s and 1960s for Algeria's independence from France. He became foreign minister at the age of 25, and stood up to the likes of Henry Kissinger at the height of the Cold War, when Algeria was tethered to the former Soviet Union.
Bouteflika famously negotiated with the Venezuelan terrorist known as Carlos the Jackal to free oil ministers who were taken hostage in a 1975 attack on OPEC headquarters in Vienna and flown to Algiers.
Most crucially, he helped reconcile Algeria's citizens after a decade of civil war between radical Muslim militants and Algerian security forces left some 200,000 people dead in the 1990s and nearly tore Algeria apart.
During his 20 years in office, age and illness took a toll on the once-charismatic figure. Corruption scandals over infrastructure and hydrocarbon projects have also dogged him for years and tarnished many of his closest associates.
Algeria has been a key partner to the United States and Europe in fighting Islamic extremism. The recent political crisis caused concern among Western allies.
Elaine Ganley and Angela Charlton contributed.
Adamson reported from Paris.