West Ham appeared to be leading the race for Fletcher before the Scotland captain opted to sign a two-and-a-half-year contract at WBA, with a 12-month option on the mid-season transfer deadline day.
Upon the completion of his move to the Midlands, an excited Fletcher, 31, expressed his gratitude to Pulis.
"It feels great. This is a fantastic new challenge for me in my career," Fletcher told WBA's official website after ending his 20-year association with United.
"I've spent my career at Manchester United and it's all I've ever known.
"But I felt it was the right time to move and I'm not sentimental about doing that - I have great memories obviously, but I'm now a West Bromwich Albion player and I cannot wait to get going.
"Everyone involved in making the deal happen has been fantastic. And a big reason I'm here is because of the head coach.
"He has impressed me from the first minute. When someone shows how much they want you it's a great feeling."
