Kightly finalised his move to the Britannia Stadium on Wednesday afternoon after agreeing personal terms and completing a medical.
The 26-year-old has spent five years at Wolves, and will provide competition for Jermaine Pennant and Matthew Etherington.
"There is nothing better than to have strong competition in all areas of the squad and Michael's arrival will give us that in the wide positions," Pulis said.
"I've long been an admirer of Michael, not only in terms of him being a provider, but also the fact that he gets his share of goals.
"Our two wingers, Matthew Etherington and Jermaine Pennant, have been brilliant for this Football Club over the past few years, but they went off the boil in terms of goalscoring last season, so we wanted to address that.
"Competition for places will bring the best out of them again and that is what Michael's presence will give us in that area."
Kightly, meanwhile, is delighted to be staying in the Premier League following Wolves' relegation last season.
"It's a great club; an established Premier League club, so I am delighted to be here," he said.
"Any footballer wants to play at the highest level and I am grateful to Stoke for giving me the chance to stay in the Premier League.
"The Club sold itself to me. What they have achieved over the past few years has been remarkable. Then there's the excellent facilities and, of course, the supporters. So, it's definitely a Club that is moving in the right direction."
Stoke are also finally in a position to complete their capture of Cameron after he was granted a work permit at an appeals hearing at the Etihad Stadium in Manchester on Wednesday.
"We are delighted the appeals panel have approved the work permit and we are now in a position to conclude the transfer," said chief executive Tony Scholes on the official club website.
"It's been a difficult period between agreeing the transfer deal and the hearing, most difficult for Geoff in particular because his life has been on hold.
"Thankfully though, we have now progressed to a point where Geoff can focus on the start to his career at the Britannia Stadium."
Scholes and Pulis made the point that Cameron, who joins from Houston Dynamo, is currently a first choice for the national side.
Scholes added: "Geoff has also been in the MLS All Stars XI three times in the past five seasons, voted by his peers as one of the best.
"In those other two seasons when he wasn't selected, one was his rookie year and the other he was injured."
