Sanllehi had held the role since February 2018 when Ivan Gazidis left for AC Milan.
Sanllehi, who was previously a director at Barcelona, initially arrived at the Emirates Stadium as head of football relations.
His replacement, Vinai, has been at the club since 2010 but was promoted to become the club’s managing director two years ago.
Sanllehi, who described Arsenal as a "true footballing institution", said: "I am proud to have been part of its history and I thank Stan and Josh Kroenke for this opportunity.
"Working with Vinai, we have built a top team for the future. Mikel [Arteta] has made an extremely positive impact since his arrival [as head coach] and has formed a strong team with our technical director, Edu.
"The academy is in very safe hands with Per [Mertesacker], and Huss Fahmy is a talented and highly-capable leader of our football operations.
"Personally, I now look forward to taking some time off and spending time with family and friends before setting to work on a new challenge and cheering Arsenal on to great things."
Owners Stan Kroenke and son Josh said: "Raul has made a big contribution during his time with us and will always be part of the Arsenal family. We thank him for all his hard work and expertise and wish him every future success.
"We have no doubt that Vinai is the right person to take the club forward. He has shown outstanding leadership during the current crisis and is held in high regard internally and externally.
"We know everyone will rally round him so we can move forward successfully."
