Suarez led the Hondurans at the FIFA World Cup in Brazil, as they finished the group stages as one of three teams to leave Brazil without a point.
The Colombian decided against staying on earlier in July, ending a three-year stint in charge - and the Honduran FA selected Medford to replace him.
Medford, 46, has been given a one-year contract as he begins his second stint coaching a national outfit, after leading his native Costa Rica between 2006-08.
The former attacker has also had club coaching jobs at Saprissa, Leon, Xelaju and Real Espana.
Joining Medford in the coaching team will be Carlos Pavon, Arnold Peralta and Luis Velasquez.