Local media said West Brom had paid around 15 million pounds ($19.24 million) for the winger.
"A talented lad, with lots of potential and a year's experience in Germany," Pulis told a news conference. "He's not the finished article but is quick and has a good eye for goal. We're looking forward to having him involved."
Pulis said Manchester City had yet to submit an improved bid for defender Jonny Evans after West Brom rejected an initial offer last week.
"Directors are dealing with that," Pulis added. "There has been no contact from Man City for a couple of days. Jonny's still a West Brom player. We can still get the situation resolved with Jonny and move on.
"Arsenal were interested last summer for Jonny but we have received no offer from them yet."
The Baggies are looking to sign another centre back and have been linked with Tottenham Hotspur's Kevin Wimmer and Ben Gibson of Middlesbrough by the British media.
"Whether Jonny goes or not, centre-half is one of four areas to fill. I could say (Kevin) Wimmer, (Ben) Gibson, someone else. But Nothing's been done so we can't talk about it," Pulis said.
"There's four more positions we'd like to bring people in. Stressful two weeks for managers, players, supporters."
Pulis confirmed Evans was still recovering from a hamstring injury and would miss Sunday's Premier League visit of Stoke City.
The Baggies have won their first two league games against Bournemouth and Burnley without conceding a goal.
(Reporting by Hardik Vyas in Bengaluru; Editing by Peter Rutherford)
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