The constituency-by-constituency estimate predicts the Tories would win 339 seats, giving the governing party a majority of 28.
The result is down on the 68-seat majority that the same YouGov MRP exercise predicted Johnson would end up with only two weeks ago.
YouGov said the surprise element of tactical voting and the tightening in the polls meant a hung parliament could not be ruled out.
The estimated result, if it materialises, would still give the PM the largest Tory majority since the 1980s, topping John Major’s 21-seat margin of Commons control in 1992.
For Labour, the prediction of winning 231 seats would be its worst result for more than 30 years, said YouGov.
Jeremy Corbyn’s party would fall from 262 in 2017 to 231, according to the newly-published research.
The Tories are predicted to take 43% of the vote and Labour 34%. The same YouGov MRP modelling correctly called 93% of seats in 2017.
If the YouGov predictions bear out, the SNP would win 41 seats and Liberal Democrats 15.
Nigel Farage’s Brexit Party is predicted to be winless after the General Election on Thursday.
According to the poll, Plaid and the Green Party will see no change from four and one seats won in 2017 respectively.
YouGov has interviewed approximately 100,000 people about their voting intentions in the past seven days.
The poll is seen as significant as it accurately forecast the hung parliament in the 2017 general election, and even correctly projected that marginal seats including Kensington and Chelsea and Canterbury would swing from the Conservatives to the Labour Party.
YouGov used a computer model known in the polling industry as MRP (or multilevel regression and post-stratification), which analyses the specific demographics of each seat.
There are signs that Labour is “patching the cracks” in its so-called “red wall” of seats across the North and the Midlands – but seats such as Don Valley, Bishop Auckland, Wrexham and Great Grimsby are still predicted to go blue.
The seats of Chipping Barnet and Putney look to be swinging to Labour, say the pollsters.
Jo Swinson’s Lib Dems are on course to win in Richmond Park, St Albans and Winchester, while also likely to win back ex-leader Nick Clegg’s Sheffield Hallam seat.
YouGov also suggested Labour has witnessed a “late rise”: “Whilst in 2017 they started to close the gap a few weeks out from the election, and then stayed steady for the final week, this time it does seem like the gap is closing very late in the campaign.”
It says since the weekend, the Conservative lead over Labour has shrunk from 11% to 9%, which has also brought down the estimated size of the Conservative majority.
Chris Curtis, YouGov’s political research manager, said: “Our latest and final poll shows that a small Conservative majority is likely, with the Tories taking 22 more seats than in 2017 and Labour losing 31.
“This would be the best and worst results respectively for each party since the 80s.
“But the margins are extremely tight and small swings in a small number of seats, perhaps from tactical voting and a continuation of Labour’s recent upward trend, means we can’t currently rule out a hung parliament.
“As things currently stand there are 85 seats with a margin of error of 5% or less.”