Vydra, who will wear number 20 for the club, said manager Steve Clarke played a big part in convincing him to choose the Hawthorns from a variety of offers.
"I didn't know a month ago if I was coming back to England but I am very pleased to become a West Bromwich Albion player and I will do my best for the team," he said.
"There was a lot of club interest from around Europe and England but I choose West Bromwich Albion because of the manager.
"He is one of the best managers in England and plays a European style.
"I spoke briefly to my former coach (Gianfranco) Zola on the telephone and he advised me to go to West Bromwich Albion because the style of play will suit me.
"I think it is a good choice for me. Another reason I chose West Bromwich Albion is because it is a great opportunity to play alongside a big striker like Nicolas Anelka."
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