During Tuesday's vote, 59 members of parliament backed Pashinyan's candidacy, and 42 voted against him.
Rock star Serj Tankian of the band System of a Down earlier joined crowds.
On the 10 consecutive day of non-protest rallies in Armenia, lead by Ter-Petrosian, the government announced an emergency situation, and supressed the peaceful protests by brutal force on March 1, 2008, killing 10 and wounding hundreds of peaceful protestors.
"All people are equal before the law".
"I would like to wish you that you form the government as soon as possible and engage in the solution of all the issues which face our state, government, entire people and this country - the Republic of Armenia. That's it. Full stop", he said. "He is one of the few political guys in Armenia who really changed", said Samvel Martirosyan, a specialist in internet security and a veteran political observer. They included 13 lawmakers representing Sarkisian's Republican Party of Armenia (HHK).
The Russian president, Vladimir Putin, was among the first to congratulate him.
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Azerbaijani Foreign Ministry spokesman Hikmet Hajieyv issued a statement insisting "the Nagorno-Karabakh region, which is now occupied, has always been an integral part of Azerbaijan". On both occasions, Pashinyan was the only candidate.
Pashinian, in a speech to parliament before his election Tuesday, said his revolution will lead to the "recognition of realizing the rights of Karabakh to self-determination".
A central square in the capital, where Pashinyan's supporters gathered to watch the voting on huge television screens, erupted into joy when the result was shown. "Long live freedom, long live the Republic of Armenia, long live we and our children who already live in free and happy Armenia", the PM said. "School teachers are free, local administrations are free".
Tankian's appearance came the evening before a parliamentary vote that was expected to see Pashinyan elected as prime minister.
In a referendum in 2015, Armenia adopted constitutional changes to move the powers from the president to the prime minister.
On 22 April he held a brief meeting with Mr Sargsyan but was then detained when the talks collapsed.
Pashinyan declined to shed light on the composition of his cabinet when he spoke to reporters moments after being elected prime minister. To elect him, it was necessary to get at least 53 votes.