The Third Division club secured the services of Lewis Sloan from East League club Dalbeattie Star in midweek.
Cox, who has signed a two-year deal with Annan, joined Montrose in January but had his contract cancelled after suffering a second red card.
He had spent more than five years with Kilmarnock, the club where Sloan also started his career.
Annan describe Cox as a pacy, versatile player who can play in midfield as well as on the wing and up front.
Source: BBC Sport
Source: BBC Sport