The Frenchman was appointed as coach of Saudi Arabia in July 2019 and led the country to a famous 2-1 win over eventual winners Argentina at the World Cup in Qatar last year.
SAFF said in a statement on Twitter that it had agreed to terminate Renard's contract at his request, adding that it wished him "every success in his future career".
"(Renard) has an offer from the French federation and expressed his desire to take this opportunity," SAFF President Yasser Al-Misehal told Saudi Sports Channel (SSC).
"We were informed four days before the current international window and I received a letter from the French Federation, and consulted with a number of members of the board of directors, and we decided to accept this request."
"We achieved great success in the qualifiers, we topped the group ahead of Japan and Australia, and we qualified for the World Cup," Renard said of his time in charge of Saudi Arabia.
"We had a great experience, and the Argentina match will remain immortal in the minds of the Saudi fans."
There were messages from Saudis to Renard too.
"Our coach and teacher, Herve Renard," Salem Al-Dawsari, who scored the winning goal against Argentina, posted on Twitter.
"Thank you for every moment you spent with us, thanks for every effort you made for us, and thanks for everything you gave us."
The former Morocco, Zambia and Ivory Coast coach took Saudi Arabia from 68th in the FIFA rankings to inside the top 50 at 49th.
Al-Misehal said there was no hurry to replace Renard with no matches scheduled until at least September when the team will start its preparations for the new World Cup qualifying campaign and next year's Asian Cup.
"We won't choose the successor until June," he said. "The Saudi national team is an ambitious and great team and we will certainly be coveted by many distinguished coaches."
French soccer federation (FFF) sacked Corinne Diacre (48) earlier this month after captain Wendie Renard (32) said she would not play at the World Cup if the coach remained in charge.
Ranked fifth in the world, France will be looking to win a first World Cup at this year's showpiece, which is being co-hosted by New Zealand and Australia from July 20-August 20.
Renard said after a 2-1 friendly loss to Bolivia in Jeddah on Tuesday that he felt he had taken the Green Falcons as far as he could.
"I would like to thank everybody in Saudi for their support during almost four years," he told reporters.
"I think I did the maximum with the team. I can't reach another level so I prefer to be honest with everybody. Thank you again, it was fantastic time."
"I wish you success in the 2024 Asian Cup in Qatar. I will support you, and certainly, if I could be present in the stands, I would be a fan of the Saudi national team," he said in a farewell video.
"You will always remain in my heart."
