The duo were absent for the Welsh club's closing pre-season friendly against Villarreal, which ended in a 3-0 defeat, but are back in contention for the trip to Old Trafford to face Manchester United on Saturday.
Dyer's wife went into labour prior to Saturday's match and the couple were then able to celebrate the arrival of their new son Shea.
Routledge, meanwhile, missed out with a minor foot injury, but is back in training after having an injection to cure the problem.
The pair face renewed competition for places in Garry Monk's starting XI this season following the arrival of Ecuador World Cup star Jefferson Montero.
The return of Dyer and Routledge leaves Swansea with just three injury worries ahead of the top-flight curtain-raiser, with Leon Britton, Marvin Emnes and Jay Fulton all suffering with knee complaints.
