The 21-year-old forward joined Leeds from York City in November 2017 but Edmondson has now signed for League Two side Carlisle United on a two-year-deal.
Edmondson had one year left on his deal at Elland Road but was released to complete a free transfer to the Cumbrians.
Leeds, though, hold a sell-on clause in the deal.
Edmondson has had loan spells away from the Whites at Aberdeen, Northampton Town, Fleetwood Town and Port Vale.
PERMANENT DEPARTURE: For Ryan Edmondson from Leeds United in a move to League Two side Carlisle United. Photo by YE AUNG THU/AFP via Getty Images.