It is the first time that the venue has been used for a Davis Cup tie, though the Centre has staged an ATP Challenger tournament for the past three years.
The tie, to be played on carpet, will be a first-round match in the Euro/African Zone Group Two, which Britain, with Greg Rusedski and Tim Henman in their squad, are expected to win next year.
To gain promotion to the Euro/African Zone Group One, Britain must beat Slovenia, then either Ghana or Malta away in July and probably Egypt at home in September.
Steffi Graf claimed her eighth title of the year when she survived a strong challenge from the unseeded Lori McNeil to win the Advanta Championship final in Philadelphia, 6-1, 4-6, 6-3.
Graf, who won the French Open, Wimbledon and the US Open, said: "It's the best year I've ever had, even better than in '88 when I won the Grand Slam. The competition is better now. There were difficult tournaments, difficult circumstances this year."
Thomas Muster and Michael Chang replay their French Open final on the opening day of the ATP World Championships, which begin in Frankfurt today.
Other confrontations in today's round-robin group matches, featuring the world's top eight players, are the world No 1 Pete Sampras against Yevgeny Kafelnikov and Boris Becker against Wayne Ferreira.