Lawson becomes the fourth team-mate to Verstappen since Australian Daniel Ricciardo chose to leave Red Bull at the end of 2018.
Perez followed Pierre Gasly and Alex Albon in being dropped for failing to convince Red Bull their performances were an acceptable level for a second driver.
Horner said: “There’s no doubt that racing alongside Max, a four-time champion and undoubtedly one of the greatest drivers ever seen in F1, is a daunting task, but I’m sure Liam can rise to that challenge and deliver some outstanding results for us next year.”
Lawson made his F1 debut at the 2023 Dutch Grand Prix as a substitute for Ricciardo, who broke his hand in a crash in practice at Zandvoort.
He scored a point for 10th place in only his third grand prix in Singapore before Ricciardo returned for the final four races of the season.
Ricciardo had originally been put in the car to establish his credentials to return to Red Bull alongside Verstappen, but he was dropped and replaced by Lawson after this year’s Singapore Grand Prix.
Lawson has out-qualified Tsunoda only twice since he returned, for the sprint races at the Sao Paulo and Qatar Grands Prix, and was on average 0.077 seconds slower over one lap.
But Red Bull have never been convinced that Tsunoda, who is at Racing Bulls at the behest of engine supplier Honda, had what it takes to be a suitable driver for the senior team.
His day in a Red Bull at the post-season test in Abu Dhabi did not change their minds.
A combative drive from Lawson at the United States Grand Prix to ninth place, where he got the better of Aston Martin’s two-time world champion Fernando Alonso, and a battle with Perez in Mexico City that ended in contact, are among the performances that have convinced them he is worth a chance.
His other points finish was another ninth place, after qualifying fifth, for the wet Sao Paulo Grand Prix – two places behind Tsunoda over both one lap and the race distance.
Lawson said: “To be announced as a Red Bull Racing driver is a lifelong dream for me, this is something I’ve wanted and worked towards since I was eight years old.
“It’s been an incredible journey so far. I am super excited to work alongside Max and learn from a world champion, I have no doubt I will learn from his expertise. I can’t wait to get going.”
Frenchman Isack Hadjar, who finished second in Formula 2 this season, is expected to join Racing Bulls alongside Tsunoda