The Yorkshireman has had a good start to life as Test captain, having overseen home wins against South Africa and West Indies.
With the historic Ashes series taking place in Australia in November, Strauss, now the England and Wales Cricket Board (ECB) chief, believes Root can join him in the elite list of previous skippers who have achieved wins Down Under.
"Certainly for me it was my greatest moment as an England captain, and I think Joe will be incredibly motivated to do that early in his captaincy career," Strauss said, as quoted on the Daily Mail.
"He's got a great chance, and he's started brilliantly. He's shown that he's very much his own man, he's got his own way of thinking about the game and that will stand him in very good stead in Australia."
Only four England captains including Strauss have led their sides to Ashes victory in Australia since the mid-1950s.
In what will undoubtedly be the biggest test of Root's captaincy so far, Strauss added that the high-pressure five-Test series will see the 26-year-old be deemed responsible for whatever happens on the pitch.
"It's the biggest challenge an England captain will ever have," Strauss added. "You are living in this incredible bubble for a long period of time, and everything is directed towards you in terms of being responsible for what's happening on the pitch."
"But also the conditions in Australia are very changeable from one venue to another, to different periods in the game and you need to be able to adapt to those conditions you see in front of you."
The Ashes will begin on 23 November as the five Test matches will be spread over a seven-week period, with the series ending on 8 January.