The Spanish two-time Formula One world champion has been linked with a move away throughout the year, with McLaren seemingly his most likely destination.
Ferrari were yet to comment on the speculation, but Di Montezemolo confirmed the 33-year-old's departure on Wednesday.
"Fernando is leaving for two reasons," he told RAI.
"One, he wants another environment. Two, because he is an age when he cannot wait to win again.
"He was disappointed that he has not won over these last years and wanted new stimulus."
Alonso is reportedly considering a move to McLaren or taking a year off with the hope of joining Mercedes in 2016.
He is without a race win in 2014, sitting sixth in the drivers' standings.