"This will certainly be a new challenge and I'm looking forward to playing my part," Brown told the Wrexham website.
Former Watford, Weymouth and Grays Athletic defender Cameron Mawer is also expected to join Wrexham manager Dean Saunders at the Racecourse.
Gareth Taylor and Andy Fleming are back in Wrexham training, although they have yet to agree new contracts at the club.
Former Wales Under-21 midfielder Jamie Tolley is one of a number of trialists at the Racecourse.
Source: BBC Sport
Source: BBC Sport