Pulis was announced as Alan Irvine's successor at The Hawthorns on Thursday and watched on from the stands later in the day as his new club claimed a 1-1 draw at West Ham.
Irvine was sacked after a run of seven defeats in nine matches left West Brom perilously close to the relegation zone.
The club find themselves a point above the bottom three following their draw at Upton Park, but now boast a boss who has never been relegated in his managerial career.
After establishing Stoke City as a top-flight club, Pulis masterminded an impressive surge to safety by Crystal Palace last season.
Brunt told West Brom's official website: "With the position that we find ourselves in at the minute, I don't think that there is a better guy for the job.
"The players have all met Tony and he has told us what he expects from us as a group and as individuals. He said that we aren't a million miles away, and all the players know that.
"I know a few lads who have played under him in the past who have been impressed, his record speaks for itself.
"He was in the dressing room yesterday and he seems very hands on, he is here to do a job and that is to get points on the board and help us climb the league.
"He was very positive when he spoke to us and he also told us what he wanted to do. I don't think that there will be any grey areas with him, which is a good thing because having grey areas costs teams points in this league.
"I'm sure that we will get lots sorted over the next few weeks on the training ground and hopefully we will start rising up the table."
Pulis will take charge of West Brom for the first time in Saturday's FA Cup tie against Conference side Gateshead, before facing Hull City in the Premier League the following weekend.
