Last week Northern Ireland boss Michael O’Neill turned down an offer to take charge, instead agreeing a new deal to remain in his current role until 2024.
“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 released by the SFA.
“While it has been tough, I am proud to leave having overseen a period of significant change and substantial growth.”
Gordon Strachan left his position as Scotland manager in October after failing to qualify for the 2018 World Cup in Russia, stretching Scotland’s wait to participate in a major tournament to more than 20 years.
The SFA must also decide later this year whether to renew a lease expiring in 2020 to continue playing Scotland’s home matches at Hampden Park or move to the home of Scottish rugby at Murrayfield.
“I recognise that it is now time for further change,” added Regan, who has been in his post for seven years.
“I have decided to step aside to allow new leadership to take the organisation forward.”
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