Johnson guided Scotland to third place during this year's RBS 6 Nations after taking the reins on a temporary basis following Andy Robinson's departure from the role.
For the time being Johnson will continue to lead Scotland's senior side, with Jonathan Humphreys assisting him during this summer's quadrangular tournament involving South Africa, Samoa and Italy.
And after discussing his new role with Scottish Rugby's chief executive Mark Dodson, Johnson admits he's relishing the role.
"I'm delighted that the discussions I've had with Mark have reached such a positive conclusion," he said.
"I've really enjoyed working with the players throughout the past year and I'm looking forward to that continuing with our quadrangular tournament in South Africa next month.
"The Director of Rugby job excites me. It's about making a really positive contribution that will stand Scottish Rugby in good stead for years to come and I am looking forward to the challenge of the new role as well as continuing with the Scotland team.
"There are some big areas such as coach development, player development, sevens and player acquisition, where, working with colleagues throughout Scottish Rugby, I want to do my bit to ensure we make best use of the talents we have to take the game in this country forward."