Yildirim received all but two of the 5,271 votes cast, a record, during the Istanbul sport club's general assembly, the club said in a statement.
The Fenerbahce boss is in prison awaiting a verdict in his trial, which includes dozens of other defendants, on match-fixing charges.
"I believe that I will be able to thank you in person for the infinite faith you have shown me and the rest of the management," Yildirim said in an acceptance note posted to the Fenerbahce website.
Yildirim, who was first elected to the three-year post in 1998, has said the trial is politically motivated on the part of Prime Minister Tayyip Erdogan's government.
Fenerbahce were runner-up this year after main rivals Galatasaray clinched the title last week.
The scandal has tarnished Turkey's multi-billion-dollar football league, and European football's ruling body UEFA barred Fenerbahce from the Champions League this year because of its alleged involvement.
Turkey has Europe's sixth-biggest football economy, the Turkish Football Federation (TFF) has said. The TFF last month officially bid to host the 2020 European Championships.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.