Burrows will officially begin at Aberdeen on February 27.
He has spent over 15 years at Motherwell FC, nine as CEO.
During his tenure, Motherwell transitioned to fan ownership, recorded its highest ever turnover and net profit and achieved a record transfer fee.
Aberdeen Chairman Dave Cormack said: "Alan has all the experience and qualities you’d look for in a chief executive. He’s got his finger firmly on the pulse of the Scottish game, is well-respected in footballing circles and is fully aligned with the strategy and vision we have to drive Aberdeen FC forward."
Aberdeen had hoped to hire a CEO in 2019 but the Covid pandemic and the subsequent financial difficulties caused a change of plan.
Burrows said: “When I decided to step down from my role at Motherwell, I was fortunate enough to have a number of clubs make contact with me. However, I was most intrigued by the Aberdeen opportunity, as I think there is so much potential at this club and so many exciting projects already well underway.
“There is much to do, on and off the pitch, and I am excited and eager to work with the many talented staff who I know are in place at Pittodrie.”
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