Lennon confirmed that Ledley, who joined Celtic from Cardiff City in 2010, had turned down a new contract so the club had no option but to accept a bid.
"A bid from Crystal Palace for Joe Ledley has been accepted and it's now down to Joe and his representatives," BBC Sport quotes Lennon as saying.
"Our contract offer was there for a long time. We made Joe an offer but they weren't forthcoming and now the ball's in their court."
Ledley has scored three goals in 50 caps for Wales.