According to the SVT Valu exit poll, which is based on interviews outside polling stations with 13,709 voters, the four left-wing parties look set to win a combined 51.3 percent of the vote compared to 46.8 percent for the right-wing bloc, a solid lead of 4.5 percentage points.
A rival exit poll published by TV4 gave the left-wing opposition a slightly smaller lead of 4.3 points.
The result, if confirmed, would be a victory for Social Democrat leader Magdalena Andersson, who became Sweden's first-ever female prime minister in 2021, a crushing disappointment for the far-right Sweden Democrats, and a relief for the ailing Liberal Party.
Tommy Möller, a politics professor at Stockholm University, predicted that the election was now in the bag.
"There is a big difference between the two government alternatives," he told TT. "If you compare the result to previous exit polls, it looks like it is done and dusted."
Alice Bah Kuhnke, an MEP for the Green Party, was the first senior politician to claim victory.
"It looks like the Swedish people have given their message and that they are tired of Tidö," she said.
The exit poll gave the Social Democrats 28.4 percent of the vote, would be only a tenth of a point above its result in 2018, which was the party's worst result in over a hundred years.
Moreover, Andersson will only be able to return to power if she can resolve the conflicting demands of the Left Party and the Centre Party, or find support among other parties, meaning she faces gruelling negotiations ahead.
The poll gives the Sweden Democrats only 17.2 percent of the vote, a 3 point drop on its result in the 2022, marking the first time the party has lost ground in an election since it entered parliament in the 2010 election.
If confirmed, this would postpone leader Jimmie Åkesson's ambitions of gaining ministers in the government with hands-on control of the party's most important policy areas, and also see the party overtaken by the centre-right Moderate Party as the largest party on the right.
It marks a respite for the Liberal Party, which had been polling well below the 4 percent threshold to enter parliament, but gained 5.4 percent in the exit poll.
The Moderates lost ground, with the 18.1 percent in the exit poll one point below what it gained in 2022.
All the other parties gained ground on 2022, led by the Green Party which increased its share of the vote by 2.4 percentage points to 7.4 percent, the Centre Party, up 0.8 percent at 7.5 percent, the Left Party, up 1.3 percent at 8 percent, and the Christian Democrats up 0.8 percent at 6.1 percent.
In the campaign, Andersson, who has steered her party to the right on immigration and crime, voting for many of the right-wing Tidö government's most hardline reforms, has campaigned in the election on promises of heavily subsidised dental care and more generous sick leave.
Sweden's Prime Minister, Ulf Kristersson, meanwhile, has promised to put 5,000 kronor a month into the pockets of the average family with a combination of tax cuts and reduced fees for day care.