Now, Verstappen has overtaken the 22-year-old Portuguese as well.
"I can only say that I have never enjoyed a season as much as this year in DTM with BMW and Red Bull," da Costa, also involved in the new Formula E series, wrote on Instagram.
"(DTM is) such a hard series full of pro drivers. May another 10 years come, and best of luck to this kid Max Verstappen," he added.
Da Costa also sent out his best wishes to Carlos Sainz jr, who until Verstappen's surprise contention at Toro Rosso was expected to make his F1 debut in 2015.
"To you my friend Carlos Sainz, I have been there," said da Costa. "Just keep pushing because that's what you're seriously good at!"
The Spanish sports newspaper Marca claims that, following promising meetings recently between 19-year-old Sainz, his famous namesake and father and Dr Helmut Marko, the Sainz duo is now confused about the future.
Another Spanish newspaper, AS, said that in the wake of Verstappen's signing, Sainz jr met again with Red Bull's Marko on Wednesday.
"The meeting was positive," said the driver, currently comfortably leading the competitive Formula Renault 3.5 series.
"Red Bull wants to support me and are trying to find a solution, even for next year," added the 19-year-old Sainz.