Mr Sargeson's position was believed to be under scrutiny following the arrival of ex-Laurel boss Ian Payne as executive chairman.
Three months ago Laurel's owner, R20, brought in Mr Payne to beef up its acquisition efforts, although the consortium led by R20 failed to successfully bid for Mitchells & Butlers earlier this month.
Laurel meanwhile underwent a major divisional restructuring programme recently, a process overseen by Mr Sargeson.
A number of other senior Laurel management, including financial controller Nigel Stock, are also believed to have resigned.
Mr Sargeson confirmed to thepublican.com that he had left Laurel but said he was currently not in a position to give any details as to the reasons for his departure.
Mr Payne is expected to take on the role of chief executive until a replacement is found.