The Spanish winger, who joined in the summer of 2013 from La Liga side Sevilla, has reached the end of his contract having made 77 league starts in sky blue plus 46 appearances from the bench, scoring four goals.
In addition, the 31-year-old also made more than 50 appearances in all other competitions, claiming four goals in the League Cup.
Having won both the UEFA Cup and the Copa del Rey twice in his native Spain, Navas enjoyed plenty more success once he moved to City.
He was a key part of the side which secured the Club’s second Premier League title in 2013/14 – his first season in Manchester.
That campaign also brought League Cup glory for Navas and City, with the Blues memorably defeating Sunderland 3-1 at Wembley in the final.
Navas – who was part of the Spain squad that won the World Cup in 2010 as well as the European Championship in 2012 - enjoyed more Wembley success in the League Cup in 2016, being part of the City side that lifted the trophy after a dramatic penalty shoot-out win over Liverpool following a tense 1-1 draw after normal and extra time.
Though renowned for his blistering pace down the right wing, Navas also demonstrated his versatility this term by being deployed at right back by Pep Guardiola on several occasions.
Commenting on Navas’s time at City, director of football Txiki Begiristain said: “Working with Jesus has been a pleasure.
“His hard work, dedication, professionalism and desire to win have been apparent every single day.
“He showed his versatility numerous times this season, operating at full-back and doing so with distinction.
“I wish him all the very best with his next move.”