Number 10 Biggar has not featured in Wales' opening two rounds, a comprehensive win over Scotland and a narrow loss to England, due to a shoulder problem, but he returns to earn his 61st cap.
Fellow British and Irish Lions Williams and Halfpenny also make the team, the former having featured and scored for Saracens against Sale Sharks on Friday to step up his comeback from an abdominal injury, while the latter was a late withdrawal against England due to an infected foot.
Winger George North remains among the replacements with Gareth Anscombe also on the bench, but Rhys Patchell – singled out as a weak link by England coach Eddie Jones before the match at Twickenham – misses out altogether, as does Josh Adams.
Taulupe Faletau does not make the matchday squad despite having been declared available on Monday in a fully-fit squad.
TEAM NEWS Wales welcome back @lionsofficial trio Dan Biggar, Leigh Halfpenny and Liam Williams for #IREvWAL. Croeso nol i Lewod Halfpenny, Williams a Biggar i wynebu Iwerddon dydd Sadwrn. pic.twitter.com/MDgRyrrmGM
— Welsh Rugby Union (@WelshRugbyUnion) February 20, 2018
"It is great to be able to bring so much experience back into the starting XV and into the backline," head coach Warren Gatland, who will take charge of Wales for the 100th time, said about his selection for the match in Dublin.
"It is the first week we have had everyone in the 'green' in terms of availability which is a nice luxury to have and a positive ahead of what is a very important Test match against a very good Ireland side.
"We have been pleased with the depth we have developed in the back three and pleased with how those players have gone, but having the experience of Dan, Liam and Leigh coming back in is hugely important.
"We have been pleased with how the forward pack has been going and how they have worked as a unit but as always there is pressure for them to perform too."
Wales XV: Leigh Halfpenny, Liam Williams, Scott Williams, Hadleigh Parkes, Steff Evans, Dan Biggar, Gareth Davies; Rob Evans, Ken Owens, Samson Lee, Cory Hill, Alun Wyn Jones, Aaron Shingler, Josh Navidi, Ross Moriarty.
Replacements: Elliot Dee, Wyn Jones, Tomas Francis, Bradley Davies, Justin Tipuric, Aled Davies, Gareth Anscombe, George North
Photo Getty Images. Caption: Wales fly-half Dan Biggar