Kentucky Coach John Calipari made the announcement at the Barclays Center, where he was accompanied by Maryland Athletic Director Kevin Anderson, Barclays Center developer Bruce Ratner and Barclays Center CEO Brett Yormark.
The 18,000-seat arena is still under construction but is scheduled to open in September 2012 and serve as the new home of the NBA's Brooklyn Nets.
Nets vice president Barry Baum told the New York Daily News that Calipari approached the team months ago and asked to have his team play the first college game in the new arena.
"It seemed like a great opportunity to have two storied programs play," Baum told the Daily News.
Kentucky is 7-5 all-time against Maryland. The schools have not met since the 2001-02 season, when the Terrapins beat the Cats 78-68 in the Sweet 16 round of the NCAA Tournament at Syracuse, N.Y.
Calipari made Wednesday's announcement in Brooklyn the morning after No. 2 Kentucky beat No. 12 Kansas 75-65 at New York's Madison Square Garden in the inaugural Champions Classic.
"We've played in the Garden and now we're going to be playing in Brooklyn," Calipari said. "We appreciate the opportunity. We will bring 10, 12,000 fans, maybe more. They'll overrun the building."
In addition to the Barclays Classic, Kentucky will also play in the Champions Classic again in 2012-13.
The venue changes from Madison Square Garden to the Georgia Dome in Atlanta, where Kentucky will play Duke on Nov. 13, 2012.