"Vogts, unfortunately, said that he did not see a future with the Azerbaijani national team," the Association of Football Federations of Azerbaijan (AFFA) said in a statement on its website.
"He said that the team had lacked assertiveness in their last game (a 6-0 loss to Croatia in a Euro 2016 qualifier on Monday).
"There was also the problem of physical conditioning. He has pointed this out on a number of occasions over the last few years, but a decision was never taken to fix this."
Abdullayev offered Vogts an opportunity to continue working with the national team but he declined, and his successor has yet to be named.
Vogts, who led Germany to victory at Euro 1996, took over as head coach of Azerbaijan in April 2008 and helped them earn a record nine points in their qualification campaign for the 2014 World Cup.
The 67-year-old was also in charge of Azerbaijan's first three qualifying matches for Euro 2016, Group H defeats to Bulgaria, Italy and Croatia.
(Editing by John O'Brien)
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