"I would like to thank Carlos for all his efforts over nearly three Formula 1 seasons", said Toro Rosso team boss Franz Tost.
In a post on his Instagram account on Saturday after qualifying for the Japanese Grand Prix, Palmer announced he would be leaving the team after the Suzuka weekend.
Given Renault's push to get Sainz into Palmer's seat early, the Spaniard is widely expected to make an early move up for the next race in Austin, potentially freeing up a place for Daniil Kvyat to return to Toro Rosso.
Frenchman Pierre Gasly steps up to a full-time drive for the rest of the season with Toro Rosso.
"First of all I would like to thank Toro Rosso and Red Bull for allowing me the possibility of finishing this season with Renault Sport Racing", said Sainz.
"When I'm heading back on the plane maybe it will sink in that I'm not driving for Renault again and maybe not in Formula 1 again". It's a shame for me to not finish the season having been with the team for a while, but I respect the decision and I wish the team the best for the future - I wish Carlos the best.
"I needed to risk at the start and it didn't work".
Toro Rosso boss Franz Tost thanked Sainz for his three years at the Red Bull junior team and quipped: "We look forward to beating him on track!"
While his vehicle has been riddled with reliability issues, he has also made several costly driver errors and he has recorded just one points finish, at the Singapore GP.
"On my side, I will definitely do my very best in tomorrow's race... this would be the best possible send-off!"
Gasly and Kvyat are now likely to form Toro Rosso's 2018 driver line-up, although Pascal Wehrlein is considered an outside contender.
Neir Renault nor Carlos Sainz wanted to wait any longer.
"The driver I am today, compared to the driver I was in 2015, is a more complete and better one, and this is thanks to Toro Rosso, who are a great group of professionals".