The Blues and Denmark U21 international have a verbal agreement in place for a six-year contract with the option of a further 12 months.
Jorgensen will undergo a medical in the United States, which is where Chelsea currently are for their pre-season tour.
New boss Enzo Maresca wants the 22-year-old to immediately join the group upon signing and he could feature by the end of the tour.
Should everything go to plan, Jorgensen could become the seventh new arrival at Chelsea this summer as talkSPORT understands they are also set to sign defender Aaron Anselmino from Boca Juniors.
The west London side have already made notable signings in Tosin Adarabioyo and Kiernan Dewsbury-Hall.
Omari Kellyman, Marc Guiu, Renato Veiga and Caleb Wiley have also been confirmed as fresh arrivals ahead of the new season.
Jorgensen is set to be the fourth goalkeeper to sign for Chelsea since Todd Boehly and Clearlake Capital completed their takeover in 2022.
After making 44 appearances for Villarreal, he will join Gabriel Slonina, Robert Sanchez and Djordje Petrovic at Stamford Bridge.
Chelsea also still have Kepa Arrizabalaga on their books after his loan spell at Real Madrid, although reports have linked him with an exit.
Marcus Bettinelli, Lucas Bergstrom and Eddie Beach are three other goalkeepers who are listed in the first-team on the club’s website.
The Blues are already underway in their pre-season schedule after they drew 2-2 with Wrexham during the week.
Their next test comes on Saturday night against Celtic, who beat Premier League champions Manchester City 4-3 in their last game.
Club America, City and Real Madrid are their final opponents in the States before a friendly against Inter Milan at Stamford Bridge.
Chelsea could be set for more transfer business from now until the start of the season, including potentially more sales to follow exits that include Ian Maatsen, Omari Hutchinson and Thiago Silva.
Maresca’s first competitive match in charge comes against his former club City on August 18.
They will then play the first leg of their Europa Conference League play-off during the following week, with the draw yet to be made.
