Twenty seven-year-old Beirne replaces the injured Iain Henderson in Ireland's engine room for the game.
It sees head coach Warren Gatland making no changes from the side which defeated Scotland at the weekend.
Jones said on Thursday that Wales were "starting to look a bit tired" after making "more tackles than anyone else in the tournament", and were facing an Ireland side "that seems to be peaking at the right time". He's played pretty often against the second rows.
"With that combination I do think he's as ready as we can get him to be at this stage".
Sean O'Brien returns to the back row in place of Josh van der Flier, who limped off early in the win over Les Bleus.
Schmidt said O'Brien had something to prove after a poor performance in the unimpressive win over Italy which led to him being left out against the French. "And I know he's incredibly motivated to be as ready as he can be".
Ireland: Rob Kearney, Keith Earls, Garry Ringrose, Bundee Aki, Jacob Stockdale, Jonathan Sexton, Conor Murray; Cian Healy, Rory Best (captain), Tadhg Furlong, Tadhg Beirne, James Ryan, Peter O'Mahony, Sean O'Brien, CJ Stander.
Wales are bidding for a third Grand Slam under Gatland - it would be a record for any Five or Six Nations coach if his players accomplish it - and also leave them in great shape six months before their World Cup challenge in Japan.
For both Best, who turns 37 in August, and Schmidt it will be their final Six Nations bow.
His theory is based on the amount of defending Wales have been required to do in the championship but Gatland, who will become the first coach to claim three Grand Slams if his team beat Ireland, has told Jones to butt out.