He had been under pressure after his side finished the year with just one win in their last seven games.
The former Real Madrid and Tottenham Hotspur manager, who returned to Malaga for a second spell in charge in May, had been under pressure after his side finished the year with just one win in their last seven games in all competitions.
Malaga president Abdullah Al-Thani, a member of the Qatari royal family, hinted Ramos had resigned in a Twitter message he sent last week but the club had not until now confirmed his departure.
"Thanks a lot Mr. Juande Ramos I appreciate your candor I #respect your decision I wish you every success," Al-Thani wrote.
Malaga said in a statement that Ramos "ceases to be the leader of the team from today (Tuesday) after the signing of an agreement between both parties".
"Juande Ramos and the club have resolved in an amicable way the contract that brought together both parties ?- for this season and two more - and today sealed the deal," the club added.
"Malaga would like to thank Juande Ramos for his work and honesty and wishes him all the best in the future in both his professional and personal life."
The team was booed by some fans after they were eliminated from the Copa del Rey in the last 32 on December 20 following a 4-3 home defeat to second-tier club Cordoba, the result sealing a 6-3 aggregate loss.
Heading into the Spanish winter break, Malaga are in 11th place in La Liga with 21 points from 16 games.
"I believe that playing games with the tension of the last matches does not help the team," Ramos wrote in a letter posted on his Twitter account.
"Football is very volatile and in the face of adverse situations the coaches tend to be those who suffer the most. In this particular case, I have decided to disconnect from a situation that bothers me and does not satisfy me."
Malaga resume their La Liga campaign away to Celta Vigo on January 7.
Ramos, 62, had previously led the club during the 2003-04 season.