Rangers' McKay received his first senior call up for the Tartan Army this week.
National team boss Strachan handed McKay his first senior call up ahead of the upcoming friendly matches against Italy and France, after the winger scored nine goals and made another 12 for the Light Blues this season.
Despite making his debut in the Premiership four years ago and going on to appear 41 times in the fourth tier the following season, McKay's ascent hasn't happened overnight.
The 21-year-old was loaned out to Championship clubs Greenock Morton and Raith Rovers during the two intervening campaigns, before Mark Warburton restored him to the first team last summer.
And Strachan has been impressed by McKay's desire to go out and get games - suggesting that is not always the way with some players.
"I love that, absolutely love it," the 59-year-old told the Sun. "That says a lot about him.
"I love all that kind of stuff, somebody who is determined to decide his own future, to mould his own future rather than sit back. I have been at clubs where you can’t get kids out. They don’t want to go. They are quite comfortable sitting there.
"Then they find out in five years’ time why they’re not playing top-level football. But I love what he’s done."
Strachan had earlier confirmed what McKay alluded to previously, that the Rangers star's performance in last month's Scottish Cup semi-final was one of the main reasons behind his call-up.
McKay caught the eye with a superb strike from distance which put the Light Blues ahead in the first half of extra time.
The Bhoys later equalised through Tom Rogic, but Warburton's men prevailed in the subsequent penalty shoot-out.