The Colombia international has left Goodison Park after just one year as he leaves for the Middle East, where he will work under former France player and coach Laurent Blanc.
A statement from Everton read: "James Rodriguez has left Everton to sign for Qatari club Al Rayyan for an undisclosed fee.
"The 30-year-old Colombia international moves to the Middle East after 12 months at Goodison Park.
"Having joined from Real Madrid in September 2020, James made 26 appearances in all competitions for Everton last season, scoring six goals."
Rodriguez was told by new manager Benitez he was not in his plans after taking over from Carlo Ancelotti, who brought in the South American having worked with him at Real Madrid.
He had not featured in a matchday squad for Everton after he was told he was behind the other players in terms of match fitness.
Summer moves to Porto and Turkish side Basaksehir failed to materialise and Benitez admitted a couple of weeks ago it would be difficult to now offload the club's highest earner, on a reported £200,000 a week.
The Colombia international joined the Toffees for £12million last summer and initially made a great impression at Goodison Park, starting the campaign with a flurry of goals and assists.
Earlier this summer, the Colombia ace compared his situation at Everton without Ancelotti as similar to that of Sergio Aguero, who joined he Catalan club this summer with the hope of playing with Messi.
According to El Espanol via Sport Witness, Rodriguez said: "Kun Agüero went to Barcelona, and now Messi is leaving. They just happen to be little breadsticks, partners.
"Those are the things that football has. The same thing happened to me. I go to Everton, practically because Ancelotti was there and look, now Carlo is gone.
"I don't know what is going to happen. In football and in life, we don't know anything. Let's see what happens."
talkSPORT Selector
Win a share of £25,000+
Pick a Premier League team to win each week
Entries cost £10
18+, Please gamble responsibly, gambleaware.org
Sign up here