MRI scans on Sunday confirmed the news after both players were injured in Saturday's draw with Carlton.
"We had our worst fears confirmed this afternoon when the MRI results confirmed both Jason and Courtenay had sustained ACL injuries," Essendon general manager of football operations Paul Hamilton said.
"Both players can expect to undergo surgery within the next two weeks but we will now proceed to determine what the best course of action is for both players and their longer-term futures."
In better injury news for the club, scans revealed no damage to Mark McVeigh’s hand following an injury in the same match.
"We are pleased with the results of the scans to Mark’s hand. We now expect Mark to be available to play in the much anticipated Anzac Day match next Monday," Hamilton said.
Winderlich went down at the 18-minute mark of the first quarter of Saturday's draw with Carlton at the MCG and Dempsey followed less than 10 minutes later.
Winderlich twisted his knee in an innocuous incident involving no other players when he was chasing the ball in the Bombers' forward 50.
He crashed to the turf and required the stretcher cart to be moved from the field.
Dempsey's occurred when he landed awkwardly after a marking contest against Jeff Garlett in the Bombers' defensive half.
Two Essendon trainers had to carry the backman from the field as the stretcher cart was still occupied with Winderlich down in the rooms.
Both players clutched their left knees and were unable to bear weight on their legs after the injuries occurred.
They both returned to the ground later in the game - Winderlich at quarter time and Dempsey in the second half - sporting leg braces and aided by crutches.
