Zelensky, who shot to fame playing the president on Ukrainian television, won the second round run-off runoff with 73.2% of the vote despite having no political experience with an anti-corruption, anti-oligarch message.
The tally broadly reflected earlier exit poll results.
While polls suggest his party will obtain a majority, Zelensky will need to seek a coalition partner to govern.
After Zelenskiy's offer, a senior member said Voice was open to an alliance with new political forces so long as they were not backed by oligarchs.More news: Iraq arrests suspect in killing of Turkish diplomat
"You know our main priorities. they are the same as those of every Ukrainian, I'm sure - to end the war, secure the return of our prisoners and victory over the corruption that still remains in Ukraine". The head of state said this at the polling station after he voted.
The rock star smiled and gave the thumbs-up as he cast his ballot, saying: "I voted for the future, I voted for new politics".
Many voters have been disappointed at the slow pace of change and sliding living standards since that time.
Both Zelensky and Vakarchuk packed their parties with young people new to politics and banned candidates who had previously served as lawmakers.More news: Hundreds rally for 'martyrs' in Sudan
"I believe that Russians and Ukrainians are one people. one nation, in fact", Putin said in an interview with the American film director Oliver Stone on June 19.
Zelensky said after the exit polls that he would "be pleased to invite Mr. Vakarchuk for talks" on forming a coalition.
More than 20 parties fielded candidates. The two met for talks in Russian Federation just days before the vote.
The Western-backed country of 45 million people has gone through two popular uprisings in two decades and is still mired in the conflict with eastern separatists that has claimed some 13,000 lives. Sporadic fighting continues along the frontlines, with four Ukrainian soldiers killed by sniper fire and mine blasts since Friday.More news: Expedition 60 crew launches to space station on Apollo 11 anniversary
Of the seats being filled, 225 members are elected from nationwide party lists, while the rest are directly elected in their districts.