The four-time Olympic champion had been coached by Salazar at the Nike Oregon Project for the past six years.
During that time, he has also being crowned world champion six times.
Salazar is currently under investigation by the US Anti-Doping Agency (Usada) after allegations about drugs use at the US training base.
But Farah, who will now with Paula Radcliffe’s husband and former coach Gary Lough, will return to London as he admits being away from his family proved too much.
“I’m not leaving the Nike Oregon Project and Alberto Salazar because of the doping allegations.
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“This situation has been going on for over two years, if I was going to leave because of that I would have done.
“As I’ve always said, I am firm believer in clean sport and I strongly believe that anyone who breaks the rules should be punished.
“If Alberto had crossed the line I would be out the door but USADA (US Anti Doping) has not charged him with anything. If I had ever had any reason to doubt Alberto, I would not have stood by him all this time.
“I’m leaving simply because my family and I are moving back to London.
“We all loved spending our summer here and Tania and I realised how much we have missed spending time with our friends and family – and the kids are so happy here, too.
“We want the kids to grow up in the UK. It’s the right thing to do for my family. But both Nike Oregon Project and Alberto are based in the USA, so it just would not be possible to continue our relationship from London.”