The Australian will step up from his role as senior assistant coach to take caretaker charge following Andy Robinson's resignation last month.
Scotland's Six Nations campaign begins on February 2 against England at Twickenham.
SRU chief executive Mark Dodson confirmed a global recruitment for a permanent successor to Robinson is ongoing.
Robinson stood down after three and a half years in charge on November 25 following the 21-15 loss to Tonga which left Scotland 12th in the International Rugby Board world rankings following 10 losses in 13 Tests.
Former United States Eagles and Ospreys head coach Johnson, who was once in caretaker control of Wales, was appointed as part of a coaching overhaul following the 2012 Six Nations, when Scotland lost all five Tests.
The 50-year-old helped to oversee the successful summer tour to Australia, Fiji and Samoa before November losses to New Zealand, South Africa and Tonga.
Dodson said: "Scott has a wealth of experience of international rugby, which was instrumental in his appointment earlier this year as our senior assistant coach.
"He has coached with Australia, Wales and the USA and knows what it is to prepare teams to win on the international battleground.
"Scott knows our players and coaches well and is determined to hit the ground running with a successful Six Nations Championship."
Johnson said: "It's an honour to take charge of the national team for our imminent campaign.
"I will be doing everything I can to bring the best out of our players as we all seek to achieve winning performances."
The coaching team remains the same, with an appointment of an interim forwards coach soon to be made; ex-England flanker Robinson formerly looked after the pack.
Assistant coach Matt Taylor (defence) and specialist coaches Duncan Hodge (kicking and catching) and Massimo Cuttitta (scrummaging) are also part of the coaching team.
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