Noureddine Bedoui, a Bouteflika loyalist and the current interior minister, was made prime minister and charged with forming the new administration, according to Algerian state news agency APS.
"We were waiting for the Algerian power to find a ruse to stay in place", said North Africa analyst Khadija Mohsen-Finan of the French Institute for global and Strategic Affairs, suggesting this is exactly what happened.
He also promised an interim leadership structure to oversee the new vote.
The statement cited Bouteflika's "health and age" as reasons he would not seek a fifth term in office, oddly claiming "there has never been any question of it" even though he refused to bow out of the race until the protest movement forced his hand.
Bouteflika postponed the April presidential election Monday and withdrew his candidacy. On Sunday, he returned from two weeks in Switzerland for medical treatment. This was the principal demand of the hundreds of thousands - possibly millions - who marched peacefully through cities and towns across Algeria on Friday in protests on a scale not seen for decades.
Protesters wave Algerian flags and hold posters opposing Algeria President Abdelaziz Bouteflika's bid for a fifth term in Paris Sunday.
Algeria's powerful military is expected to play its traditional behind-the-scenes role during the transition and is now considering several civilians as candidates for the presidency and other top positions, political sources said.
Algerians told the Dzair News channel they wanted "full change" to the government rather than "superficial regulations" as announced Monday by President Abdelaziz Bouteflika.More news: Hollywood stars among dozens charged over college entrance scam
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But on Tuesday, there was more skepticism over his decision to delay an April 18 election without setting a new date, which opponents say could leave him in power indefinitely.
"I welcome the decision by President Bouteflika, which is the start of a new page in the development of Algeria's democracy", Macron told a press conference during a visit to Djibouti in east Africa.
His opponents said they did not believe he was in a fit state to run the country, an OPEC oil producer, and suspected he was being kept in place to protect the grip of the military and business elite.
Algerian officials had said days ago that Bouteflika was expected to return shortly.
"What's most important today is the Algerian street massively wants change", Mohsen-Finan added.
After posting a message of "victory", engineer Akli Ourad called for "vigilance, vigilance" on Facebook, saying Bouteflika's promise was merely "a gimmick" aimed at winning another year in office.
Many Algerians were concerned about his ailing health, and anxious that his death in office during a fifth term might cause risky political instability.