Costelow missed the narrow 16-14 loss to England in their previous game two weeks ago with a neural neck injury but returns in the team that coach Warren Gatland (60) named on Tuesday.
Cardiff eighthman Mackenzie Martin (20) was named among the substitutes for the first time and is in line for his first cap if he comes on against the Irish.
Wales are looking for their first success in this year's Six Nations but are up against a rampant Ireland, who have won both their opening fixtures in this year's tournament.
"We are excited to go out to Dublin and test ourselves against one of the leading sides in world rugby. It's a challenge we are relishing," said Gatland in a statement.
"We've made steps in the last couple of games and now it's about building on that, learning from those experiences and taking that into this weekend.
"It's about continuing to work hard, looking for accuracy in our performance across 80 minutes and also keeping our discipline," the coach added.
Gatland had made seven changes ahead of the England clash after Wales went down at home to Scotland in an opening 27-26 loss.