South Korea was among the first countries to hold a national vote since the pandemic began.
Strict safety and social distancing measures were in place for the vote.
With nearly all votes counted, Mr Moon's Democratic Party won 163 seats in the 300-seat National Assembly.
The party's sister group, the Platform Party, was forecast to win a further 17 seats, giving the government a total of 180 seats.
Among the winning candidates for United Future was high-profile North Korean defector Thae Yong-ho. Mr Thae, a former senior diplomat at North Korea's embassy in London, won a seat for the Gangnam district in Seoul.Although 35 parties put forward candidates, the race was between the left-leaning Democratic Party and the conservative opposition, United Future Party. United Future and its parliamentary partners are expected to win 103 seats.
It is the first time in 16 years that left-leaning parties have secured a majority.