Rangers raised eyebrows in Scottish football last month by hiring the Liverpool legend on a four-year deal.
Gerrard, 38, had never managed a senior team before, having done a stint coaching the Reds' academy sides after ending his illustrious playing career.
Nevertheless, Stubbs, who was appointed St Mirren boss this week, has praised the Englishman for having the "balls" needed to take on such a big job without much experience.
He told Deadline News: "I had a text from him a couple of days ago to wish me all the best, which was nice, and I said the same to him.
"Knowing Steven, the type of character he is, he’ll be absolutely relishing the challenge.
“Did I see it coming? No, but good luck to him. I admire his bravery more than anything – it shows balls. Privately he’s had a few offers to go in, not felt they were right, but he’s jumped in now. I think he’ll find it eye-opening.”
Gerrard's mandate in Scotland is simple: overhaul Celtic, who have won back-to-back domestic trebles under Brendan Rodgers.
It's a huge ask for the former Los Angeles Galaxy ace, but Rangers fans will be hoping that Stubbs is right and that Gerrard is equal to the challenge.