Several hundred people gathered in front of the central post office in downtown Algiers, the capital, on Tuesday night after his announcement.
The crowd was peaceful, singing songs and waving Algerian flags while drivers passing by honked horns in celebration.
Hours before his resignation, the country's powerful army chief issued an extraordinarily blunt statement that demanded the President leave office immediately.
Bouteflika's resignation came a day after his office announced on state media that he would step down before April 28th.
That short statement carried on state television also said that Bouteflika would take steps to "ensure state institutions continue to function during the transition period".
The statement, which offered few details, heightened concerns among many Algerians that Bouteflika was seeking to anoint a hand-picked successor, remain politically active behind the scenes and ensure his clique stayed in control of the country.
Students today took the streets in protests.
Within Algeria's powerful military establishment, there was also concern.
Earlier today, Vice Defence Ministry minister and the army's chief of staff, General Ahmed Gaid Salah, held a meeting with senior defence ministry officials and top commanders.
He proposed applying articles in the constitution to declare Bouteflika unfit and remove him from office.
"Our decision is clear and irrevocable," said Salah, demanding that Bouteflika vacate office immediately.
"We will support the people until their demands are fully and completely satisfied."
Salah added that "there is no longer need to waste further time" and that the constitutional measures to unseat Bouteflika should be undertaken immediately.
Those remarks added intense pressure on the President to step down.
- additional reporting AP
