Coulson, 24, moves to Bootham Crescent after turning down a new contract offered by the Mariners.
He had been with them since moving from Barnsley during the 2009-10 season, scoring 16 goals in 72 appearances.
McReady is only 19 but played 37 times for Darlington last season and scored against York in a 2-2 draw in January.
The pair join Oli Johnson and Lee Bullock in moving to Bootham Crescent as the Minstermen prepare to return to League Two, having won promotion from the Blue Square Bet Premier last season.
Source: BBC Sport