Farah, 34, said he was moving back to London, leading to his split from Salazar after more than six years working together.
The British long-distance runner said he would team up with Gary Lough, who has coached wife Paula Radcliffe.
"I'm moving back home, London, I really miss home," Farah said in a video posted on Twitter.
"Seeing my kids the way they were in the summer at the World Championships, I'm going to be back there. I'm very excited.