Venkatesham has been at the club for 14 years and was made chief executive in 2020.
He has explained it was time for him to “pursue another challenge”, with Arsenal now having a chance to appoint his successor to take over next summer.
Venkatesham is committed to the club until then and remains focused on his role.
He said: “This was a tough decision, but it is time to pursue another challenge. Now is not the time for goodbyes as I remain focused until my last day and supporting a seamless transition.”
Arsenal’s Co-Chair Josh Kroenke added: “The Board is fully supportive of Vinai’s desire to pursue his next challenge.
“Whilst it is business as usual with everyone focused on the season ahead, we’d like to take this moment to thank him for his contribution and long service.
“Vinai will always be part of the Arsenal family and always welcome back at Emirates Stadium.
“Change and succession is something the club is well prepared for.
“The Board remains committed to our strategy and will address leadership change as we continue to drive the club forward.”