Regan, 53, took up the position in 2010 and leaves the association having recorded its highest ever profit in 2017.
However, he has been unable to find a successor to Gordon Strachan as manager of the national team, who have not qualified for a major tournament since the 1998 World Cup in France.
Strachan left by mutual consent last October after Scotland failed to qualify for this year's World Cup in Russia.
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"I have devoted my time in Scotland to modernising, protecting, developing and promoting the game, whilst facing into some extremely challenging head winds during my time in the job," Regan said in a statement.
"While it has been tough, I am proud to leave having overseen a period of significant change and substantial growth...
"We are now at another staging point and I recognise that it is now time for further change. I have decided to step aside to allow new leadership to take the organisation forward."
Regan came in for criticism and questioning from his colleagues for his handling of the search for a new Scotland manager. Northern Ireland boss Michael O'Neill was courted but turned down the position last month.
The SFA said chief operating officer Andrew McKinlay will manage the day to day business while it searches for a new chief executive.
Former Scotland assistant coach Mark McGhee told talkSPORT radio station on Thursday that Strachan should succeed Regan in the role.
(Reporting by Christian Radnedge, editing by Ed Osmond)
