Newly-elected SA president Barclay Nettlefold said Neil's exit was a "mutually agreed departure" but it's understood he was informed on Friday he would be stood down from the role.
Neil's exit comes four days before he was due to front the review into the London Games campaign, but it's expected he'll still take part in the review.
SA board member Jeremy Turner will serve as interim chief executive and it's likely Neil's successor will be appointed after the review.
"We will now examine what primary areas of expertise the new CEO is required to have to meet the immediate and long-term vision of the sport," Nettlefold said in a statement.
Nettlefold said Turner is not seeking a full-time appointment.
The former Canberra Raiders NRL club boss was appointed to SA's board of directors in February 2008 then later in the year took over from Glenn Tasker, who resigned after six years as chief executive.
Australia's London Games team failed to produce an individual gold medal for the first time since the 1976 Olympics despite high expectation for the likes of world 100m freestyle champion James Magnussen.
That disappointment came after Australia won six swimming gold medals in Beijing 2008 and seven in Athens 2004.
While the initial focus was on issues of funding and training, SA called an independent review and the team's attitude was called into question as allegations of bullying and aggressive behaviour were made public.
Tommaso D'Orsogna, a member of the Australian men's 4x100m freestyle relay squad, revealed in September he and teammates had behaved like "schoolboys" in camp before the Games.
D'Orsogna also claimed some squad members were "putting themselves up higher than the rest of the team".
Veteran Leisel Jones, who retired last week, said she had confronted teammates who were "bullying" a young teammate at the London Olympics.
The SA board was expected to wait until the completion of the review before deciding on a replacement for Neil.
SA was expected to hold a press conference on Thursday to announce Neil's resignation.