The governing FIA said that the 21-year-old, whose father and namesake was twice world rally champion, had been examined at the circuit medical centre at the Olympic Park circuit and passed fit.
"All the medical checks are positive for Carlos," team principal Franz Tost told reporters. "He feels very well, he feels very strong and therefore I don't see any reason not to allow him to go to the start."
Sainz had been listed already at the back of the provisional starting grid, next to the McLaren of compatriot Fernando Alonso and behind fellow-Spaniard Roberto Merhi, after Toro Rosso sought permission from the stewards for him to take part.
He was released from hospital on Saturday evening after escaping serious injury in a crash that raised safety concerns after his car ended up with the linked plastic Tecpro barriers piled on top of it.
"My back and my neck are just a bit sore from the accident, but I’m totally ready," he had said after leaving hospital.
On Sunday, surrounded by a media scrum in the paddock, he said he still felt stiff but "nothing that a painkiller cannot kill.
"I will start the race and if I cannot move my neck or something I will stop. I feel perfectly capable of doing the start and participating in the race."
Tost said Sainz had approached Turn 13 at around 307kph in final practice before braking.
Just before that, the 21-year-old rookie had changed the brake mapping which led to the rear tyres locking under braking and loss of control.
"He was always fully conscious, he also switched the engine off and he did all the procedures absolutely right...that was also important for the decision (to race)," said Tost.
"Of course the impact was quite heavy but he was checked yesterday at the hospital in Sochi and they couldn't find anything."
(Editing by Patrick Johnston/Amlan Chakraborty)
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