The protests mobilised a wide range of people, from students, journalists, lawyers, unions and the influential association of veterans of the war of independence against the French between 1954 and 1962.
Bouteflika, who is 82, has barely been seen in public since a 2013 stroke.
He relented on Monday by announcing he won't run again and said presidential elections scheduled for April 18 will be postponed indefinitely. Perhaps not yet. A new constitution has been promised, but no timetable has been set. A cabinet reshuffle will happen soon, a statement in Mr Bouteflika's name said.
The election process was thrown into chaos on Monday when the current President bowed to the pressure of weeks of mass demonstrations, promising a transition to a new government.
The conference will be accompanied by a national referendum to rewrite the constitution.
Bouteflika has named interior minister Noureddine Bedoui as the new prime minister to replace the unpopular Ahmed Ouyahia.
Meanwhile, Lamamra was appointed deputy prime minister.
Brahimi, a former foreign minister and United Nations special envoy, is expected to chair the conference, the source told Reuters.
"Justice must keep its distance from political tensions", he said.
Algerian government plane heads north, destination unclear
The army will likely rely on respected figures like Brahimi, and old friend of Bouteflika, to mediate.
Watch: Thousands in Montreal protest Bouteflika government:Huge crowds gathered outside the Algerian consulate in Montreal to protest the country's ruling government and to stand in solidarity with people in the north African country amid what's being called the "Algerian Spring".
Algeria's election had been slated for April 18; Bouteflika said the vote will be delayed to ease apprehensions and "pave the way for spreading serenity, tranquility and public security".
Thousands of Algerians shared the same concerns that the decision is just a way to allow Bouteflika to stay in power for an indefinite period.
"It's a very important moment because power in Algeria has never backed down", said Benjamin Stora, a leading historian of Algeria. "The battle is not won". "This will be a sleepless night", said 25-year-old Abdelghani Hachi.
High school students face riot police officers as they protest in Algiers, Algeria, March 12, 2019.
Bouteflika's pledge, a day after he returned from Switzerland where he spent two weeks at a hospital for medical checks, failed to convince his key rival Ali Benflis.
A declaration by judges yesterday that they would refuse to oversee the election seems to have been the final straw.
"The protests that changed his mind have shattered years of political inertia and unsettled Algeria's opaque but powerful security establishment", NPR's Eleanor Beardsley reports from Paris.