"Craig is probably the most experienced goalkeeper at this level and performs consistently," he added.
Brechin have brought in Scott Morrison on a short-term deal to provide cover for the Glebe Park outfit.
Nelson, 39, spent a season on loan at Brechin in 2004 before signing a permanent deal the following year and has been with the club ever since.
He counts Hearts, Partick Thistle and Ayr United among his former clubs.
Source: BBC Sport
Source: BBC Sport