Sportal.co.nz 20.Dec.2012Getty Images
Johnson was hired by the Scottish Rugby Union in June as senior assistant to Andy Robinson, who stepped down last month following an embarrassing 21-15 loss to Tonga at Pittodrie.
The Sydney-born 50-year-old is expected to be officially unveiled later this week, with Italian scrum coach Massimo Cuttitta lined up as his assistant.
Johnson had a brief playing career in Australia with the NSW Waratahs before joining Wales as a skills coach in 2001.
He took over as head coach of Wales on a temporary basis following the resignation of Mike Ruddock in 2006 before further stints at the helm of the US Eagles and Welsh club Ospreys.
Scotland first five-eighths Greig Laidlaw told BBC Scotland that Johnson was a welcomed appointment.
"He's a very clever coach," Laidlaw said.
"In the modern game he's probably one of the best coaches I've ever worked with.
"He's laid back off the pitch but very intense on the training field.
"I believe that we have good players in Scotland. Hopefully, we can get it right and take the next step.
"With a new coach, he can refresh everybody and go from there."
Scotland, who have slipped to 12th in the world rankings, will open their Six Nations campaign against England at Twickenham on February 2.