Lawmakers voted 59 to 42 in favour of the former opposition leader Pashinyan, who had led weeks of mass protests against the ruling party.
Russian President Vladimir Putin has already congratulated Pashinyan on the appointment.
This is the second time the vote has been held. Last week, the ruling Republican Party (RPA) refused to support Pashinyan, triggering another wave of protests in the country, after which the RPA conceded to back Pashinyan's nomination.
