He had been widely expected to sign a new two-year contract, having led Al Ahli to second place in the league this season, but instead announced he would be leaving with immediate effect.
"I'm really sad ... but for me two years is my limit so I feel this is the moment to say goodbye," Flores told a news conference in Dubai.
Flores won the Europa League with Atletico in 2010 before leaving the following year after failing to qualify for the Champions League.
He arrived at Al Ahli in November 2011 and guided the club to fifth place in his first season before finishing runners-up this term, 11 points behind champions Al Ain.
Flores also won two domestic knockout competitions, the Etisalat Cup and President's Cup.
"With Quique's calibre he will always have job offers from Europe ... we tried our best to retain him," said Al Ahli chairman Abdullah al Naboodah.
"We will take a few days to put together a shortlist but it won't be easy to replace him."
Flores's exit follows that of former Italy goalkeeper Walter Zenga who ended his two-year stint at rival Dubai club Al Nasr by mutual consent earlier this month.
A few days later Sven-Goran Eriksson quit as Al Nasr's technical adviser after just four months to become the coach of China's Guangzhou R&F.
Naboodah said Al Ahli had signed Portugal playmaker Hugo Viana on a free transfer from Braga while striker Grafite had also agreed to stay for another season.
The Brazilian, player of the year in the Bundesliga four seasons ago, has scored 53 goals in 55 games since joining Al Ahli in 2011.
Chilean Luis Jiminez has two years remaining on his contract and will also stay but former Barcelona winger Ricardo Quaresma is poised to end his brief stint in Dubai, having joined Al Ahli on a free transfer in January.