Laidlaw has been handed the opportunity to impress at fly-half, where he is poised to win his fourth cap in place of Dan Parks, who yesterday announced his retirement from international rugby with immediate effect following a poor display in last Saturday's 13-6 loss to England at Murrayfield.
Edinburgh prop Geoff Cross has been recalled in place of Newcastle tighthead Euan Murray, who does not play on Sundays for religious reasons, in the only other change to the starting XV.
Uncapped Glasgow Warriors trio Ed Kalman, Duncan Weir and Stuart Hogg have been named on the replacements' bench.
Scotland head coach Andy Robinson has retained Chris Cusiter at scrum-half, with Mike Blair on the bench, opting against an all-Edinburgh combination of Blair and Laidlaw at half-back.
Parks' decision to end his 67-Test career, following 266 points and a Scottish record 17 drop-goals, means he will not return to the scene of one of his finest performances for Scotland.
The 33-year-old was man of the match when Scotland agonisingly lost to a last-gasp Shane Williams try in the 2010 Six Nations.
That game saw Thom Evans suffer a career-ending neck injury and his brother Max has been named on the wing for Scotland this weekend.
Laidlaw won his first two caps as a replacement scrum-half and made his first Scotland appearance as a fly-half in an impressive substitute performance against England - something which may have hastened Parks' decision to call time on his eight-year Test career.
The 26-year-old, nephew of former Scotland and Lions scrum-half Roy Laidlaw, is also in line to be the frontline goal-kicker, having held those duties for Edinburgh.
Robinson said: "Congratulations to Greig on his first start.
"He is a gifted footballer who is acclimatising very well to the differing demands of the stand-off position from having spent most of his career at scrum-half.
"Having lost last weekend, I believe the time is right to move on and look to develop our emerging talent at stand-off."
Weir is among those emerging talents.
He scored 20 points, including a solo try, in Scotland A's 35-0 win over England Saxons last Friday, contributing to his elevation to the Test squad. Hogg also scored a try in the match at Galashiels.
Robinson added: "I've always stressed the importance of the A team and the part that both Duncan Weir and Stuart Hogg played in the game at Netherdale last week is another reason for my continued excitement and belief in Scottish rugby."
Cross is the only change in the pack, coming into an all-Edinburgh front row of hooker and captain Ross Ford and loosehead Allan Jacobsen, with Kalman taking his place on the bench.
Richie Gray and Jim Hamilton have been named at second row, with Alasdair Strokosch, Ross Rennie and David Denton in the back row.
Outside Cusiter and Laidlaw are Sean Lamont and Nick De Luca at centre, Max Evans and Lee Jones on the wings and Rory Lamont at full-back.
Scotland team to play Wales in the RBS 6 Nations match at the Millennium Stadium Cardiff on Sunday, February 12 (kick-off 1500):
R Lamont (Glasgow Warriors); L Jones (Edinburgh), N De Luca (Edinburgh), S Lamont (Scarlets), M Evans (Castres); G Laidlaw (Edinburgh), C Cusiter (Glasgow Warriors); A Jacobsen (Edinburgh), R Ford (capt, Edinburgh), G Cross (Edinburgh), R Gray (Glasgow Warriors), J Hamilton (Gloucester), A Strokosch (Gloucester), R Rennie (Edinburgh), D Denton (Edinburgh).
Replacements: S Lawson (Gloucester), E Kalman (Glasgow Warriors), A Kellock (Glasgow Warriors), J Barclay (Glasgow Warriors), M Blair (Edinburgh), D Weir (Glasgow Warriors), S Hogg (Glasgow Warriors).