AEK have made a bright start to the domestic season but have suffered two successive defeats in the opening Europa League group matches matches, including a 4-1 loss to Anderlecht and a 2-1 home defeat to Sturm Graz.
"Manolo will always be part of the history of our club and he has linked his name with winning the Greek Cup after many years," AEK said in a statement issued after protracted negotiations over the Spanish coach's severance package.
"I believe it is time for a change to the benefit of everyone. I am therefore not saying goodbye, but see you later," Jimenez told the AEK website.
Former AEK player and coach Kostenoglou has signed a one-and-a half-year contract to take over.
Jimenez took over AEK in October last year and lead the club to a third place in the Super League last season and also won the Greek Cup with a 3-0 win over Atromitos.
Kostenoglou, 41, made over 200 appearances for AEK in an 11-year playing career from 1994-2005 while also having a brief spell as caretaker coach at the end of the 2007-2008 season. He coached Larissa last season.
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