Biggar has recovered from a shoulder injury to make his 61st appearance for his country and will line up alongside Gareth Davies at half-back.
Halfpenny and Williams join Steff Evans in the back-three with Hadleigh Parkes and Scott Williams continuing their partnership in the midfield.
Wales have named an unchanged pack for the trip to Dublin. The all-Scarlets front-row of Rob Evans, Ken Owens and Samson Lee feature for a third consecutive game. Cory Hill partners captain Alun Wyn Jones in the second-row with Aaron Shingler, Josh Navidi and Ross Moriarty comprising the back-row.
“It is great to be able to bring so much experience back into the starting XV and into the backline,” said head coach Warren Gatland, who will take charge of Wales for the 100th time.
“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.”
Elliot Dee, Wyn Jones and Tomas Francis are named as the front-row replacements with Bradley Davies and Justin Tipuric completing the forward contingent. Aled Davies, Gareth Anscombe and George North provide the back-line cover.
WALES TEAM TO PLAY IRELAND:
Leigh Halfpenny (Scarlets) (75 Caps)
Liam Williams (Saracens) (45 Caps)
Scott Williams (Scarlets) (53 Caps)
Hadleigh Parkes (Scarlets) (3 Caps)
Steff Evans (Scarlets) (7 Caps)
Dan Biggar (Ospreys) (60 Caps)
Gareth Davies (Scarlets) (29 Caps)
Rob Evans (Scarlets) (22 Caps)
Ken Owens (Scarlets) (54 Caps)
Samson Lee (Scarlets) (35 Caps)
Cory Hill (Dragons) (12 Caps)
Alun Wyn Jones (Ospreys) (115 Caps) CAPT
Aaron Shingler (Scarlets) (15 Caps)
Josh Navidi (Cardiff Blues) (9 Caps)
Ross Moriarty (Gloucester) (19 Caps)
Replacements:
Elliot Dee (Dragons) (4 Caps)
Wyn Jones (Scarlets) (7 Caps)
Tomas Francis (Exeter Chiefs) (28 Caps)
Bradley Davies (Ospreys) (59 Caps)
Justin Tipuric (Ospreys) (54 Caps)
Aled Davies (Scarlets) (7 Caps)
Gareth Anscombe (Cardiff Blues) (13 Caps)
George North (Northampton Saints) (70 Caps)
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