Last week, army chief Ahmed Gaid Salah demanded that the president step down and called for the Constitutional Council to invoke Article 102 of the Constitution. But the infirm leader - who has rarely been seen in public since a 2013 stroke and appeared pale and weak handing over his resignation letter - had always been seen as absent while an authoritarian and sclerotic clan known as Le Pouvoir ("The Power") continued to rule. That made clear that the army chief's call for Bouteflika to desist had the backing of the military - among the most important on the African continent.
However, protesters have voiced opposition to the entire system surrounding Bouteflika, calling for a complete overthrow of the status quo including the army and the Presidential alliance.
The military intends on preserving its power and influence in the government, but it also recognizes that it has a shaky relationship with the Algerian people. There are also palpable concerns that Bouteflika will simply be replaced by a clone who will maintain the same system of governance, which for Algerians has represented nothing more than corruption, nepotism, squandering of national wealth and a marginalisation of genuine political actors.
In Sudan, the organisers behind months of anti-government demonstrations welcomed Mr Bouteflika's resignation and expressed hope that their president, Omar Al Bashir, would follow. First, we now have a face-to-face between the street and the military institution.
The army has not seemed to be keen on being dragged into a conflict like the civil war that blighted most of the 1990s.
Algeria's Constitution says that when a president dies or resigns, the Constitutional Council confirms the leader's absence and both houses of parliament convene. He had a stroke in 2013 and has rarely been seen in public since.
The current upper house president is Abdelkader Bensalah, a Bouteflika ally - as is the prime minister.
Originally, the protestors demanded that Bouteflika abandon his bid for the fifth term, to which he gave in on March 26, but then quickly postponed elections in attempts to extend his rule indefinitely. That's still unclear, but the governing National Liberation Front is expected to hold a conference to discuss reforms demanded by protesters.
Bouteflika leaves the Palace of El Mouradia with no final words for a people he hardly knew.
Among those they have chastised are Ali Benflis, a former Bouteflika premier who has become one of the president's key rivals, and Abderrazak Makri of the moderate Islamist Movement for the Society of Peace.
"Our session today is related to establishing the vacancy of the post of president of the republic, following the resignation of Mr. Abdelaziz Bouteflika yesterday", said Constitutional Council president Tayeb Belaiz as he opened Wednesday's meeting of the 12-member body. "He will leave but the same regime, which has ruled Algeria since 1962 and its independence, will stay if we don't continue to protest", said Mohamed.