The Bosnian led Algeria to the last 16 of the 2014 FIFA World Cup in Brazil, but left the position following the expiry of his contract.
After qualifying from a group which also featured Belgium, Russia and South Korea, Algeria were eliminated in the second round by Germany after extra time.
Halilhodzic had long been linked with a return to Trabzonspor, where he managed from 2005 to 2006, and the Super Lig side welcomed him back via their official Twitter account on Saturday.
No details have yet been released of Halilhodzic's contract, but some reports suggest he will be officially unveiled on Sunday.
The 61-year-old's CV also includes stints in charge at Paris Saint-Germain, Dinamo Zagreb and the Ivory Coast.
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