The former Scotland striker earlier on Friday announced he would no longer be representing his country.
And 33-year-old Vancouver Whitecaps forward Miller has revealed in a statement the amount of thought which went into his decision to retire.
He said: "It is with huge sadness that I am announcing my retirement from international football.
"It has been the toughest decision I have ever made in football but I bow out with huge satisfaction and pride.
"After 12 years and 69 caps, it is time for me to fully concentrate on the remainder of my club career and dedicate more time to my young family.
"I once said I would never quit playing for Scotland but after long and careful thought, I would only be carrying on for selfish reasons and for the good of the country it is in everyone's best interests that the younger Scottish strikers take the nation forward.
"I would like to thank Craig Brown for taking a chance on me in 2001 and every other Scottish manager who I played under.
"To captain my country on several occasions was the greatest honour and memories that I will never forget.
"I would especially like to thank my mum and dad, who have supported me in fulfilling my dreams right from an early age, without them it would not have been possible.
"I am now looking forward to supporting my country at Hampden as a fan."