Miller informed Strachan of his decision on the eve of announcing his squad for the forthcoming World Cup qualifiers against Belgium and Macedonia.
The 33-year-old has left a major imprint on the national team's recent history, scoring memorable goals against the likes of Germany, Italy and England since making his debut against Poland in 2001.
The Vancouver Whitecaps striker scored 18 goals in 69 internationals but, with Scotland already out of the qualifying reckoning for Brazil 2014, he somewhat reluctantly called time on continuing to travel back from Canada to play for his country.
Strachan, who called up Ross McCormack and Jamie Mackie to his squad, said: "It wasn't an easy decision for him. I spoke to him last night and he said the reason he took so long to get back to me was because it was such a hard decision to make and he really didn't want to make that phone call.
"But he did it and we wish him good luck. When Kenny Miller packs in football, he will know he has got as much as he possibly could out of his career with the ability he had.
"He has left nothing behind in international football. It's good as a footballer when you can move on to something else knowing you have given it your best shot. It was a bit unfair because in the conversation I was trying to convince him that he should maybe try for another year or so.
"Then I thought to myself: 'This is unfair.' It was hard enough Kenny making this call without me putting extra pressure on him to think about it longer.
"Halfway through the conversation I said: 'Forget what I say, your decision has been made'. Because of that decision, his club football will go on longer. When you want to play the game that you love longer, then you have to decide whether you want to play international football or not.
"It's been done by many a great player at that age - 33, 34, 35 - and I understand why they want to do it. That's what he wants to do. He loves the game. Kenny is the marquee player for his team and he feels he is due them something for the confidence they have shown in him."
With Leigh Griffiths and Jordan Rhodes also in the squad, and Steven Fletcher set to return after making his comeback from an ankle injury in the coming weeks, Strachan has several striking options.
But the Scotland boss has regularly hailed the professionalism and work ethic that Miller brings to the squad and that could be just as much a loss as his goalscoring, which took him to sixth on the country's all-time list behind only Kenny Dalglish, Denis Law, Hughie Gallacher, Lawrie Reilly and Ally McCoist.
The final strike came at Wembley last week when he turned the English defence before drilling the ball into the bottom corner with his left foot, a goal that put Scotland 2-1 ahead before they fell to Rickie Lambert's late winner.
Strachan, who signed Miller for Celtic, said: "Everyone can be replaced but he has left a legacy in the squad to younger players - how you behave when you join an international squad, how you train, how you play.
"And also he leaves us on one of his best games for Scotland. He wasn't blessed with natural ability so he has taken whatever he has had and worked hard at it. He has made himself fitter. Because of that he has stayed in the game longer, he has become more intelligent.
"And I think it all came together in that England game, how he played, how he annoyed people, how he linked up, how he scored the goal. Because of his hard work, then he finishes off on a high note in international football. That's not just luck, that's working at it."