The 24-year-old represented Australia at under-19 level but has played first-class cricket for Middlesex since 2009 and averaged over 50 in their promotion season in 2011.
And as the Ashes were getting under way Down Under, Miller told the Times: "A lot of people have had conversations with Sam to find out where he stands, what he wants to be, and that decision has been made.
"There had to be a determination that he wants to play for England. I do not know whether or not it is there in writing, but enough people have talked to him and he has that passion."
Australia batsman Chris Rogers has been a colleague and regular opening partner of Robson at Middlesex since 2011 and said: "It is a tough one for Australia.
"Sam has probably made his decision and while I was disappointed, I can understand why he has chosen to play in England.
"He is going to be an excellent cricketer. He has the game to open the batting and the rest is up to him."
Selecting Robson would reignite the debate over the number of players born overseas playing in the England team, but Miller insists a passion for the country trumps concerns over somebody's place of birth.
"We want England to be England," he said.
"If these fellows come in and pass all the criteria asked of them and they have a determination, and I find out 'do you want to play for England?' and they pass that test, you are duty-bound to select them.
"If they have that quality, then fine. I need to know when they put those lions on it is for the lions and not for themselves."