In recent days, it has been claimed that the French champions have been planning to exercise the buyout clause in the France international's deal before it increases to €100m (£85.6m) on Monday.
Les Parisiens have been linked with a swoop for Dembele for some time, having apparently considered bringing him to the Parc des Princes in 2022 when his Barcelona future was in limbo.
Chelsea were also thought to have been interested in signing Dembele, who briefly became a free agent last year before agreeing to a two-year renewal at Barca, whose volatile economic situation prevented them from tying him down for longer.
Dembele previously stated that Barcelona were hoping to keep him on the books until 2027 and hinted that an agreement over fresh terms would be reached with the La Liga champions, but head coach Xavi has refused to rule out a summer exit for the 26-year-old.
Having asked for Barcelona's permission to speak with Dembele, Fabrizio Romano now reports that PSG have verbally agreed a long-term deal with the attacker's agent until the summer of 2028.
Romano adds that PSG have sent another letter to Barcelona informing them of the pact, and the capital giants are now thinking about the best way to finalise Dembele's arrival.
PSG's sporting project is believed to have been a key factor in Dembele's decision to leave Barcelona, where he has been blighted by injuries since joining from Borussia Dortmund for €135m (£115.6m) six years ago.
When fit, Dembele has scored 40 goals and set up 43 more in 185 matches for the Spanish champions, who apparently tried and failed to force him out of the door in January 2022 when he entered the final six months of his previous contract.
However, Dembele managed to reignite his career under Xavi with 13 assists in the 2021-22 La Liga season, while he ended the 2022-23 campaign with eight goals and nine assists from 35 games in all tournaments.
The former Rennes starlet won his third La Liga title in Barca colours last season, and he has been involved for Xavi's side in pre-season despite the ongoing speculation, scoring in the weekend's 3-0 win over El Clasico rivals Real Madrid.
Dembele may have now played his final game in a Barcelona jersey, though, as he prepares to become the latest new face to arrive at the Parc des Princes in a busy summer of spending for PSG.
The French champions have already captured Marco Asensio, Arnau Tenas, Milan Skriniar, Manuel Ugarte, Lee Kang-in, Cher Ndour, Lucas Hernandez and former youth product Xavi Simons, who has been loaned out to RB Leipzig for the 2023-24 campaign.
Dembele will further reinforce an attack which is adapting to life without Lionel Messi, while there is seemingly no resolution to the Kylian Mbappe saga as the Frenchman threatens to run down his contract.
With Real Madrid not expected to meet PSG's asking price this summer, Liverpool and Chelsea are alleged to be planning shock swoops for Mbappe, although PSG fear that he has already agreed to join Real on a free transfer in 2024.