Vancouver Whitecaps striker Miller - who has declared himself fit for Friday's clash in Cardiff after recovering from a hamstring strain - is pleased the issue has been resolved despite the increased competition.
"Steven coming back into the squad affects me, of course it does," he told the Scottish Sun. "It affects me in the sense there is now a young player - who plays at a high level, scoring goals regularly - who is part of our squad. It's competition, simple as that."
He added: "But I'm absolutely thrilled the situation has been sorted, we all are. I said before the last qualifiers, the situation had to be resolved.
"As a group, we will gladly have him play."
Fletcher has ended his international exile ahead of the World Cup qualifying double header against Wales and Belgium after the intervention of a third party helped him heal a rift with boss Craig Levein.
The in-form Sunderland forward had previously not been involved with the national team since informing the Scottish Football Association by text message that he did not wish to be selected for a game against Northern Ireland in February 2011.