There had been speculation Red Bull might call up the Dutchman to its senior team, or that the energy drink company might pull out of F1 altogether.
And boss Christian Horner this week warned any rival teams that attempts to poach Verstappen will be futile due to his watertight contract.
“I think we should be happy that Max will also drive next season at Toro Rosso,” Jos Verstappen told De Telegraaf newspaper.
“I think in our situation we are best off here,” the former F1 driver added. “Max still has much to learn and can gain experience at Toro Rosso.
“Am I relieved? I think we saw it coming,” Verstappen added, referring to the fact that Red Bull had earlier looked in danger of being pushed out of F1.
“No, I did not have any sleepless nights.”
It appears that Red Bull will not change its drivers across the board for 2016, with Daniel Ricciardo and Daniil Kvyat staying at the senior team, and Carlos Sainz to remain Verstappen’s teammate.
Turning to his father, Max commented: “I’m glad that all the drivers are confirmed now as I was afraid they might put you in there!” (GMM)