Sullivan said in a tweet on Monday: "After 18 years with the Free Software Foundation, I've decided to resign my position as executive director, effective at the end of a transition period.
"We'll be sharing further details, including information about that transition, and a few more words, in the coming days.
"It's been a humbling honour to serve this institution, and to work alongside the FSF's staff, members, and volunteers over the years. The current staff deserve your full confidence and support - they certainly have mine."
Last week, a push to oust Stallman from the FSF board began, soon after he announced that he was rejoining the board.
Meanwhile, Miguel de Icaza, co-founder of the GNOME desktop project and now an employee of Microsoft, said in a tweet: "[The] 'rms should resign' signatories list contains many significant contributors to free software – people that have had to interact with him and have advanced the cause. The rms support list seems to be mostly users with few credentials – likely fans that never had to deal with him."
He did not provide any evidence to back up his claims.
"RMS failed to grow as the movement grew. And has been an anchor dragging the project ever since. The ideas survived and flourished elsewhere. He is still a drag on every project under his direct influence," added de Icaza, a divisive figure in free and open source software circles while he was part of it.
The pro-Stallman group has mustered 3744 individual supporters, while the anti-Stallman letter has 16 main signatories, 48 companies and organisations, and 2811 individual supporters as of this morning.
Stallman announced he was rejoining the board during the FSF's annual LibrePlanet conference on 19 March.
Both Red Hat and SUSE, the two largest open source vendors, have supported the move. But while SUSE has put its name as a company to the letter calling for Stallman to be removed, Red Hat has not done so.