The rally followed weeks of protests and strikes after parliament voted in mid-April to elect former president Serzh Sargsyan as prime minister - a move seen as anti-democratic by the opposition.
Opposition politician Nikol Pashinyan is the only nominee in the vote in parliament.
The leader of the Armenian opposition faction Yelk, leader of protests, Nikol Pashinyan, was the only candidate nominated by the Yelk, Tsarukyan Bloc and Dashnaktsutyun factions for the second round of the voting.
The Armenian parliament voted 59-42 Tuesday to elect Pashinian, who headed weeks of huge protests.
Pashinian declined to shed light on the composition of his cabinet when he spoke to reporters moments after being elected prime minister. Pashinyan also promised that there would be no persecution in the country for political and economic reasons.
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Pashinyan only called an end to the rallies after the Republicans said they would back his candidacy.
"Representatives of the party will not be members of the government". There will be no people enjoying privileges in Armenia.
Vahram Baghdasaryan, head of the Republican Party in parliament, said for the sake of unity it was backing Pashinyan for prime minister but it had concerns about his fitness to run the country. He said his ministers will be chosen "as a result of discussions" with his allies and other political groups.
Pashinian went on to play a major role in a broad-based opposition movement launched by former President Levon Ter-Petrosian, the main opposition candidate in a hotly disputed presidential election held in February 2008. He was sentenced to seven years in prison in 2010 but was released the following year under an amnesty.
"The spring of liberation has come to Armenia", one Pashinyan supporter, 56-year-old Sona Paremuzyan, told AFP in Yerevan. "However, if it turns out that they are ineffective, they will be discontinued", he said. His deputy, Karen Karapetyan, was named acting prime minister. He later called off the demonstrations after the ruling party assured him of its support in his bid for prime minister.