VeeKay joins Steven Thomas, Scott Huffaker and Mikkel Jensen in the #11 Oreca 07-Gibson.
The Dutchman is set for his third Rolex 24 appearance after contesting this year's edition with Racing Team Nederland, an entry which was also run by TDS. The Dutch team finished second alongside Frits van Eerd, Giedo van der Garde and Dylan Murry.
VeeKay didn't get to drive in his 2021 debut with DragonSpeed after a crash by his teammate.
"I’m looking forward to racing at Daytona again," said VeeKay, who finished 12th for the second consecutive year in a disappointing 2022 IndyCar campaign.
"The race to second place with Racing Team Nederland was one of the best experiences I had in my racing career so far.
"Thanks to that race I’ve developed a lasting love for endurance racing. When TDS Racing approached me to race with them in next year’s Rolex 24, it was obvious for me to say yes.
"Joining Mikkel, Scott and Steven, I’m pleased to be part of one of the best line-ups of the 2023 Rolex 24.
"Mikkel has earned his stripes and nowadays acts as a factory driver with a platinum drivers’ categorisation. Scott’s a silver with a golden edge and Steven is among the best bronze drivers in the world.
"As a Racing Team Nederland driver, I got to experience how professional TDS Racing operates."
TDS will run two cars in the 2023 IMSA WeatherTech Sportscar Championship season, with VeeKay’s former RTN teammate van der Garde joining the sister #35 entry headed up by Francois Heriau.
Team manager Xavier Combet added: "We are very pleased to be able to work with Rinus again for this edition of the 24 Hours of Daytona.
"I appreciate Rinus for his professionalism and his motivation to win. Last year he showed his speed in LMP2, despite having little experience with the car. We are convinced that Rinus will strengthen the #11 entry and that, together with Steven, Scott and Mikkel, he’ll have a great chance to win.”
The Rolex 24 takes place on January 28-29, with the official Roar Before the 24 test held the previous weekend.
