Real Zaragoza have accepted a Stoke offer rising to £2.8 million for the winger.
"This is fantastic news, just what we all wanted," said Pulis.
"Jermaine has made such a big impact since he has been with us and he has become a big favourite with the supporters, so I know that everyone will be delighted that we have completed this signing.
"The important thing has been getting him comfortable and settled, and now that we have done that I am sure he can go on to play an even bigger part in our plans.
"Natural wingers are hard to come by, but we have two of them with Jermaine on the right and Matty Etherington on the left, so that gives us a real threat down both flanks.''