Fletcher took the armband from Chris Brunt for the 2-2 draw with Burnley on Sunday - the Scotland international's West Brom debut following his move from Manchester United.
Pulis insisted his decision has no reflection on Brunt’s ability in the role, instead saying Fletcher’s "stature" in the game made him the obvious choice to lead the team.
"Brunty was asked to be captain a while back I think and he took it," said Pulis. "I don't think he has ever said he wanted to be captain or anything like that. He was asked and he took it.
"I think Darren has come into the football club and he’s got a bit of stature about himself. The other players have responded very well to him.
"I always had it in my mind that it [the signing of Fletcher] wouldn't be just about him playing, it would be his influence, the way he trains, the way he works, the way he lives his life.
"He is a wonderful character and hopefully that will rub off on other people."
However, it is not just Fletcher that Pulis will be looking at to lead the team on the pitch, with other experienced players also expected to pull their weight as Albion attempt to pull away from trouble in the final months of the Premier League season.
He added: "We had a meeting this morning with the senior pros.
"I have had Brunty in there, Joleon [Lescott], Ben [Foster] and Fletch, talking about little things that I want to be implemented at the football club over the next couple of weeks.
"They are senior players, they have all played in the Premier League for a long time. Darren might be wearing the armband, we might expect a lot of him, but there are other people who can join in and contribute. That is the way I have always been."
West Brom return to league action on Wednesday when they host Swansea City.
