The team's official NBA web page has been updated, with a short, simple statement to reflect the change: "Jersey Strong, Brooklyn Ready."
The hip-hop mogul also announced that he'll headline a series of concerts -- as many as eight -- at the arena when it opens, the New York Daily News reports.
Jay-Z, whose real name is Shawn Carter, owns a small stake in the Nets, according to My Fox NY. He grew up in the Marcy Houses, a public housing complex in the Bedford-Stuyvesant neighborhood of Brooklyn.
"This is my foundation," he said in an interview with Good Day New York's Rosanna Scotto (available below).
"I'm really giddy right now," he added, clearly excited by the announcement.
The Barclays Center is being built as part of the Atlantic Yards development in the Prospect Heights neighborhood of Brooklyn. The controversial project was announced in 2004 but has been mired in delays.