The Leinster back-row returns after fracturing three vertebrae in his back in the 18-11 win over France. He replaces Jordi Murphy.
Johnny Sexton has recovered from a hamstring injury while Jared Payne and Sean O'Brien are fit after concussion.
Grand Slam-chasing Ireland top the table, two points clear of Wales.
The Millennium Stadium encounter will be a special occasion for skipper Paul O'Connell, with the Munster lock set to play his 100th Test match for Ireland.
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Ireland have named the same team which defeated France in Dublin last month.
France lock Pascal Pape was banned for 10 weeks for kneeing the Lions forward Heaslip in the back during that match.
After suffering the injury, Heaslip looked in danger of missing the remainder of the Six Nations but the number eight insists that he always remained optimistic of making a quick return to action.
"I don't personally listen to outside sources, I listen to our trusted medical team and they gave me some very good guidance," said the Leinster star.
"We mapped out a really good, clear plan, in terms of ticking the boxes in recovery and I have ticked them along the way and now I'm good to go."
Sexton was still rated doubtful on Monday and the availability of the Racing Metro fly-half is a major fillip as they prepare to face Wales.
The 29-year-old picked up his injury in the closing stages of Ireland's 10-point win over England earlier this month.
Ulster centre Payne and Leinster flanker O'Brien were concussed in the same game.
Tommy O'Donnell makes way for Murphy's place on the Irish replacements bench.
Joe Schmidt's side can take a giant stride towards a first Grand Slam in six years with victory over Wales.
Ireland are also on course for back-to-back Six Nations titles for the first time since 1949 as they aim to set a new Irish record of 11 straight Test wins.
Rob Kearney (Leinster); Tommy Bowe (Ulster), Jared Payne (Ulster), Robbie Henshaw (Connacht), Simon Zebo (Munster); Johnny Sexton (Racing Metro), Conor Murray (Munster); Jack McGrath (Leinster), Rory Best (Ulster), Mike Ross (Leinster), Devin Toner (Leinster), Paul O'Connell (Munster, capt), Peter O'Mahony (Munster), Sean O'Brien (Leinster), Jamie Heaslip (Leinster).
Replacements: Sean Cronin (Leinster), Cian Healy (Leinster), Martin Moore (Leinster), Iain Henderson (Ulster), Jordi Murphy (Leinster), Eoin Reddan (Leinster), Ian Madigan (Leinster), Felix Jones (Munster).
Ireland number eight Jamie Heaslip is back from injury to face Wales in the only change for the Six Nations game in Cardiff on Saturday.