A joint poll released by broadcasters KBS, MBC and SBS estimated that the opposition Democratic Party (DP) and its minor allies could secure between 183-197 seats in the single-chamber, 300-seat parliament, and Yoon's conservative People Power Party (PPP) and its affiliates would win 85-100.
Another poll conducted by cable network JTBC showed the opposition camp was likely to get 168-193 seats, while it put the PPP coalition on 87-111.
The bitterly fought race was seen by some analysts as a referendum on Yoon, whose popularity has suffered amid a cost-of-living crisis and a spate of political scandals.
Official results are not expected to be released until the early hours of Thursday, but exits polls in previous elections have given a broadly accurate reflection of the results.
Nearly 29.4 million people, or 66.3% of eligible voters, had cast their ballots as of 6 p.m. (0900 GMT), according to the National Election Commission, including 14 million who had voted before election day.
It marked the highest ever turnout for a parliamentary election at this point, though the numbers were down from the 2022 presidential vote that narrowly brought Yoon to power.
The exit polls indicated that the DP-led opposition, which already dominates the legislature, would increase its majority but fall short of securing a super majority of 200 seats, which would have stripped Yoon of his veto power.
But their expected landslide victory could hamper Yoon's policy efforts to boost the economy, improve fiscal health and lift record low birthrates, as well as to bolster trilateral security cooperation with the United States and Japan.
A liberal splinter party led by former justice minister Cho Kuk, which has emerged as a dark horse, was projected in the polls to win up to 15 seats and to become a third-party force that could influence control of the assembly.
Opposition leaders have accused Yoon and the PPP of mismanaging the economy and failing to rein in inflation, with Cho vowing to make Yoon a "dead duck" president by gaining sufficient seats.
PPP chief Han Dong-hoon, who had said an opposition majority would create a crisis for the country, said the exit polls were "disappointing" but said he is awaiting final results, without elaborating.
Democratic Party head Lee Jae-myung has yet to comment on the polls.
Cho said the numbers highlighted voters' desire to hold Yoon's administration accountable for what he called a "prosecutor dictatorship," referring to Yoon's previous role as prosecutor general.
Cho pledged to push for a bill to appoint a special counsel to look into alleged irregularities involving PPP chief Han's family. Han has previously dismissed such allegations.
(Reporting by Jack Kim, Sebin Choi, Daewoung Kim and Hyonhee Shin; Editing by Lincoln Feast, Ed Davies and Shri Navaratnam)

Children help their mother put a ballot in the ballot box for South Korea's general elections at a polling station in Incheon, west of Seoul, South Korea, 10 April 2024. EPA-EFE/YONHAP SOUTH KOREA OUT