The Dane finished ninth in the standings this season with his single victory coming in the Baku sprint race and took two runner-up finishes from his best weekend of the season at Monza.
Vesti, who beat Enzo Fittipaldi to win the 2019 Formula Regional European championship with Prema before stepping up to FIA Formula 3 with the squad for 2020, will join F3 graduate and Ferrari Driver Academy member Oliver Bearman as part of a revamped Prema lineup.
The Italian squad will part company with its 2021 F3 champion Dennis Hauger, who has signed for the MP Motorsport squad that took Felipe Drugovich to this year's F2 title, while Jehan Daruvala will need to find a seat elsewhere to continue for a fourth season in F2.
Vesti, 20, said he is anticipating a title challenge next year as Prema has previously launched Oscar Piastri (2021), Mick Schumacher (2020) and Charles Leclerc (2017) to the Formula 1 feeder series crown.
“To join Prema Racing for the 2023 Formula 2 season is great news for me,” said Vesti, who finished fourth in each of his two seasons of F3.
“I have known Prema since 2019 when we won the Formula Regional European Championship together.
“Prema is an amazing place to be at and in my opinion gives me the best opportunity to fight for the F2 title in 2023!
“I have big dreams and Prema is the team I believe that I can achieve those dreams with.
“There is no doubt that 2023 F2 is going to be incredibly close, but I will give my everything to be fast and consistent throughout the season.”
Prema boss Rene Rosin added: “We are delighted to welcome Frederik back. He is a quick and hard-working driver, which we already had the chance to appreciate in 2019 and 2020.
“We are obviously looking forward to joining forces again and seeing what we will be able to achieve together next season.
“With his skills and the experience he has matured, we expect him to be a contender and we are determined to support him the best way we can.”
