Terry won back the England captaincy yesterday, one year after being stripped of the armband by coach Fabio Capello.
The clumsy handling of the announcement is understood to have angered injured captain Rio Ferdinand, who first learnt of Capello's desire to return the captaincy to Terry via newspaper reports.
"[It's] just business as usual, the manager's made the decision," Milner told a press conference. "Everyone's happy for JT [Terry]. It's obviously disappointing for Rio.
"We're fortunate to have a number of leaders in this squad," said Milner, describing Terry as a natural England captain. "He puts his head in where a lot of people wouldn't. He leads off the field as well.
"The manager makes his decision and we stand behind them. JT is a leader, he might not have been captain over the last year but he's not changed the way he has been.
"The most important thing is leading on and off the field and as an England player he's been absolutely fantastic."
Meanwhile, Tottenham Hotspur striker Peter Crouch said there were no problems within the squad over Terry's return as captain. "There was a lot of talk about it. There are no problems with anyone," he said.