Smith, 33, joins the club as player-coach under new joint managers Paul Rawden and Russ Cousins.
He started the season at EVO-STIK League Premier Division rivals Matlock Town, having previously played for the likes of Chesterfield, York and Mansfield.
Coming in as goalkeeping coach is Brazilian Adriano - who made his name at Bristol City, appearing in a Championship play-off final.
Rawden said: “Both Nathan and Adriano bring in a wealth of knowledge and experience. Adriano played in the Championship Play-Off Final for Bristol City. Nathan has been around many clubs and has lots of contacts within the game.”
Completing the backroom staff also is Brian Franks, he has good knowledge of non-league football and was previously with Rawden and Cousins at Harrowby United.
Cousins added: “We’ve had a good training session last night, we’ve met the squad and plenty of those who work behind the scenes at the club.
“We’ve got a week to get our ways installed before we take on South Shields in our first match next Tuesday.
“We know the league position and we know winning matches is going to get us out of that position. We’ll be doing everything we can to make from now to the end of the season a good one.”