He has spent three seasons with the Welsh region, winning a Magners League title in that time and will be in place with the Scotland squad in time for their tour to Australia, Fiji and Samoa in June 2012.
Johnson said: "I'm excited by this challenge. Scotland is a country with a great history in rugby and with Andy there's a real focus point to get it back to where it belongs on the world stage by creating something new and brighter."
Robinson had said he wished to add an experienced international coach to his management team and is pleased to have secured Johnson.
He said: "I am delighted Scott has agreed to join the Scotland coaching team. I have huge respect for him as a coach and a person having coached against him on numerous occasions."