Barton's JMJ Holdings specializes in land development with resort projects in the United States, Mexico and the United Arab Emirates.
Bari is the most prominent team from Apulia, located in Italy's boot, along the southeastern coast.
It returns to Serie A in 2009-10 after winning its third Serie B title last season. It opens at defending champion Inter Milan on Sunday.
"This is a fantastic opportunity," Barton told the Bari website. "The Bari fans are passionate about their team and with new management we hope to grow this franchise into one of the most successful and competitive in Europe."
Texas billionaire Ellis Short recently took control of English club Sunderland, while Tom Hicks, whose Hicks Sports Group owns the Texas Rangers and Dallas Stars, is the co-owner of Liverpool, having bought the club with George Gillett Jr. in 2007.