Gerrard takes charge of his first competitive match on Thursday when Rangers host Macedonian side Shkupi in the Europa League.
But former Scotland and Celtic boss Strachan believes Gerrard has already made his mark by boosting the profile of the Scottish game.
The former Liverpool and England captain made his eighth summer signing on Tuesday when he brought in Lassana Coulibaly on loan from Angers, and the Ibrox support has been rejuvenated by his appointment after an underwhelming two seasons of top-flight football under three different managers.
Strachan, who was playing at a Prostate Cancer UK golf day, said: “He’s changed the landscape in Scotland already. The profile of Scottish football has gone up since Steven’s went along there.
“He will enjoy being the manager of Rangers. They’re a huge club, so he will love it. He’s done well for Scottish football so far.”
Strachan, who spent four years managing in Glasgow, added: “People have been asking should he have joined Rangers as they’re a big club but he might as well do that because you’re mostly judged on your first job anyway.
“He might have gone to Ipswich or Crewe and not done well there and would have had to build up his career again but he’s done the right thing going to Rangers.
“He’s helping everybody out, helping himself out and it will definitely help Scottish football out.”
Strachan was representing the League Manager’s Association, who are working with partners Prostate Cancer UK to promote awareness of the most common cancer in men, which claims the life of one man every 45 minutes.
“I think we’ve probably all been affected by the disease,” he said. “We get to the age where people round about us start having problems with prostate cancer. We can relate to that.
“When it comes to helping, I think the managers really get into it because it’s something that’s happening round about us - it’s something they can touch, something they can feel. So many friends of mine have been lucky enough to have been able to have been diagnosed early so that they’re still living fantastic, healthy lives, because we’ve actually looked after each other.”
- For more information go to https://www.prostatecanceruk.org/football