Force India did not say who the other driver would be, but that is assumed to be Canadian Lance Stroll whose billionaire father Lawrence heads a consortium that now controls the Silverstone-based outfit.
The Mexican's contract extension also effectively means highly-rated French youngster Esteban Ocon, Perez's team mate this season, will not be part of the racing line-up next year.
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Perez, 28, played a major role in events leading to the takeover of the team in August and has said for some time that he had no concerns about his future and knew where he would be racing next year.
Force India, previously co-owned by financially-troubled Indian magnate Vijay Mallya, went into administration at the end of July after Perez made a claim for $4.01 million that was owed to him.
The action was supported by the team's engine provider Mercedes and team sponsor BWT which were also owed significant sums.
The team, now known as Racing Point Force India to distinguish them from predecessors Sahara Force India, are expected to change name next year.
"I am very happy to finally announce my future and I'm really motivated for 2019," Perez said in a team statement ahead of the U.S. Grand Prix and following Mexican race.
"Force India has been my home since 2014 and has allowed me to grow as a driver and show my skills on track."
The Mexican, who joined Force India after a difficult year with McLaren after two seasons with Sauber, has had five podium finishes with the team including third in Azerbaijan last April.
The sport's sole Mexican driver has also brought significant sponsorship.
McLaren have meanwhile not had a top three finish since the opening race of 2014.
Force India team principal Otmar Szafnauer said Perez had established himself as "one of the most talented and consistent drivers on the Formula One grid.
"He gives us valuable stability going forward and is a huge asset to this team," he added.
Ocon's only remaining chance of racing in Formula One next season now rests with Mercedes-powered Williams, Stroll's current employers who have so far confirmed only Britain's Formula Two leader George Russell.
Like Russell, Ocon also has a long-term Mercedes contract and is a talent the reigning champions are nurturing for the future.
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