Farah, who won 5,000m and 10,000m gold at London 2012 and Rio 2016, said his decision was based on a desire to move back to London.
Salazar is being investigated by the US Anti-Doping Agency after BBC's Panorama made allegations about drugs use at his US training base.
He will now work with Gary Lough, who previously coached - and is married to - women's marathon world record holder Paula Radcliffe.
Salazar said he has offered to continue working with Farah in an advisory role.
