Parks ended his Scotland career with immediate effect yesterday after 266 points - including a Scottish record 17 drop-goals - and after winning the last of 67 caps in last Saturday's Calcutta Cup loss to England.
Edinburgh's Greig Laidlaw is set to inherit the number 10 jersey in the team to facwe Wales in Cardiff named, with Duncan Weir poised to be named on the replacements' bench alongside fellow uncapped Glasgow Warrior Stuart Hogg, who can play outside centre and full-back.
Robinson said: "I have really enjoyed working with Dan. He wasn't in my first Scotland squads but through his own determination, hard work, skill and competitive spirit he forced his way back into selection.
"It's never an easy decision to make but I feel Dan has made the right decision and thank him for his contribution over the years."
Parks regularly turned tight matches in Scotland's favour during an eight-year Test career which began against Wales in 2004.
However, Parks was also much maligned and his error against England - a charged-down kick which resulted in Charlie Hodgson's decisive score - will be part of his legacy.
After one of five rounds of the Six Nations, the timing of the decision could be brought into question, but Parks recognises with Ruaridh Jackson, Laidlaw and Weir emerging, it is time to hand over the number 10 jersey for good.
Parks had been contemplating retiring after the World Cup, when he was second choice behind Jackson, but the lure of the opening Six Nations clash with England was too strong. However, now his Test career has been brought to a close.
He told www.scotlandrugbyteam.org: "Now is the right time to retire from the international game.
"I have some fantastic memories of playing for Scotland and what that has meant to me. I've no regrets."
Parks becomes the third senior Scotland squad member to retire post-World Cup, following Nathan Hines and Chris Paterson.
Parks' retirement and the unavailability of tighthead Euan Murray, who does not play on Sundays for religious reasons, means there will be at least two changes to the Scotland team to play Wales.
Geoff Cross is set to come in for Murray, while Mike Blair could replace Chris Cusiter at scrum-half, in part due to his understanding with Laidlaw.
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