The Blues are forking out slightly more than the Senegal international's £30million release clause but are paying in instalments instead.
Jackson scored 13 goals last season for Villarreal and will arrive at Stamford Bridge to bolster a blunt attack.
The 22-year-old has already agreed personal terms over an eight-year contract with Chelsea are looks almost set to become their new player.
He will be the second new arrival at Stamford Bridge this summer following the signing of Christopher Nkunku, who is also a forward.
After a miserable year where Chelsea finished 12th, one of their biggest problems was a lack of goals.
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They scored just 38 times in the Premier League - only four clubs scored less than them.
No one managed to score double figures for Chelsea across the whole season with Raheem Sterling and Kai Havertz both netting nine.
And the latter, who started as Chelsea's main striker this season, is set to leave for Arsenal in a deal worth £65million.
Jackson joined Villarreal in 2019 as a youngster and made his La Liga debut in 2021.
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After playing every La Liga game last season, he scored 13 times - including nine in his last eight matches.
The forward nearly moved to the Premier League earlier this year with Southampton and Bournemouth strongly linked in January.
Jackson made his international debut for Senegal in November after coming on as a substitute against the Netherlands at the World Cup in Qatar.
Chelsea are expecting to have quite a different squad by the time the new season begins in the Premier League.
Several players are set to leave including Kalidou Kouibaly, Hakim Ziyech, Edouard Mendy, Mason Mount and the aforementioned Havertz.
New boss Mauricio Pochettino has plans to bring in a midfielder and a goalkeeper with Moises Caicedo strongly linked.
However, finding a new keeper has proved trickier after interest in Andre Onana cooled.
Valencia star Giorgi Mamardashvili has been looked at, as well as Brighton's Robert Sanchez.