The Brazilian was expected to find a new team this summer after his contract with German side Wolfsburg was due to expire at the end of June.
Diego, who spent the second half of last season on loan at Spanish champions Atletico Madrid, opened up talks with Fenerbahce last month.
The club's chairman Yildirim has now confirmed that the 29-year-old will join Fenerbahce's summer training camp in July, although the club will wait until a formal contract is signed before making an official announcement.
"We've reached an agreement with Diego Ribas. We didn't make the official statement because the signing process hasn't been done yet,” Yildirim said in Fenerbahce's financial meeting today.
“Most probably he'll join the team in July. He will be our single transfer this summer. We won't sign any player except him."
The Brazil playmaker fell down the pecking order at Atletico following his loan move from Germany in January.
Despite his lack of regular games for Los Rojiblancos, Diego scored one of Atletico’s most important goals of the season when he netted a 30-yard screamer during the club's Champions League quarterfinal tie against Barcelona at the Camp Nou.
The star thanked the Atleti fans and staff in a farewell message on social media recently and stressed he would always remain a fan of the club.
The message read: "I'd like to thank the staff, my teammates and the wonderful fans for all the kindness and courtesy they always showed me.
“It was an honour to be part of this club again, where I had the pleasure of experiencing even more special and unforgettable moments.
“I am leaving happy and safe in the knowledge that I once more gave absolutely everything to help the team. From today I am no longer an Atletico player, but I will always be a huge fan of this club!!!"