West Bromwich completed the capture 21 international midfielder Scott Allan from Dundee United on Tuesday.
Allan, 20, joins the English Premier League club on a 2 1/2-year contract, and West Brom manager Roy Hodgson was excited about the new addition.
"Scott's one of the most exciting talents in Scottish football," Hodgson said, "so why shouldn't he be part of our immediate top-flight plans?
"It would be harsh to demand of him that he steps on the training field at the start of the week and is then the best player next Saturday.
"But certainly, he'll come into the first-team squad straight away and we'll see what impact he can make."
Allan has played four times for Scotland's U-21 side and played nine times for Dundee this season.
"I'd like to wish Scott all the best for his future career - it is a fantastic opportunity for him to go down to the English Premier League," Dundee manager Peter Houston said.
"The completion of the deal at this time was beneficial for both the player and the club."
West Brom is 15th in the EPL, and host Norwich City on Saturday.