Poke, 30, joins the Spitfires until the end of the season following his release by Portsmouth.
He made nine National League appearances while on loan at the club earlier this season as injury cover for fellow goalkeeper Ross Flitney.
Coulson, 21, has signed a two-and-a-half-year deal after moving from National League South Oxford City.
The Spitfires have also agreed to loan Lewis Noice and Jack Masterton to Southern League club Larkhill Athletic until the end of the season.
Find all the latest football transfers on our dedicated page.
National League Eastleigh have signed goalkeeper Michael Poke and defender Luke Coulson.