The 60-year-old has been in the position for 11 years, and during that time the team has won the County Championship three times, most recently last summer.
In his 23 years as a Surrey player, Stewart also took home six trophies, including three Championship crowns.
He told the club website, “This has been the hardest decision of my working career, without a doubt.”
“I have dedicated myself fully to this work since November 2013, and it has been a privilege and an honor to be a part of the world’s best cricket club.
Throughout his playing career, Stewart, the 91-year-old son of former Surrey and England player and coach Micky Stewart, participated in 133 Test matches and 170 one-day internationals.
Both a brilliant fielder and an elegant batsman, he captained the national team throughout 15 Test matches. He amassed 26,165 first-class runs at an average of 40.06, with 48 hundreds to his credit.
Despite his choice to leave, he stated: “From now until my last working day, I guarantee that my commitment to the job and to the club will not diminish one bit, and I am fully focused on helping the squad achieve more success.”
He continued by saying that “other opportunities around the game that work for me and my family” would be something he would be open to pursuing.