Eight of Virginia’s Division I men’s basketball teams will compete in a holiday tournament in Richmond under a plan Gov. Bob McDonnell (R) is set to announce Wednesday, according to three people with direct knowledge of the event.

The tournament, which will be called the Governor’s Holiday Hoops Classic, will be held in the 2012 and 2013 seasons with the hope that it will become an annual event.

In December 2012, George Mason will play Richmond in the first game of the doubleheader; Virginia will play Old Dominion in the second game. The following year, Hampton will play James Madison and Virginia Tech will play Virginia Commonwealth.

Five of the eight teams earned 2011 NCAA tournament bids this year.

The event will take place at Richmond Coliseum, which is where Wednesday’s announcement will be made. Athletic directors and coaches from the participating schools will join McDonnell at the announcement.

If the tournament becomes an annual event, it is hoped that other Virginia schools with Division I men’s basketball teams will take part in subsequent years, those with knowledge of the planning said.

After George Mason advanced to the second round of the NCAA tournament in March, Coach Jim Larranaga departed the program he led to the 2006 Final Four to take the head coaching position at Miami. The Patriots hired former Georgia Tech coach Paul Hewitt, who will begin his first season at the helm in Fairfax this fall.

Virginia Tech finished last season 21-11 but was not selected for the NCAA tournament. The Hokies advanced to the second round of the NIT.

Under second-year Coach Tony Bennett, Virginia finished 16-15 this past season, which marked the Cavaliers’ first winning campaign since 2007-08. The Cavaliers were not selected to play in the NIT and declined other postseason tournament opportunities.

VCU made a stirring run to the Final Four of the NCAA tournament this past spring under second-year Coach Shaka Smart, who agreed to an eight-year contract extension at season’s end after he was pursued by several higher-profile programs.

Richmond advanced to the round of 16 in this year’s NCAA tournament before falling to top-seeded Kansas. Led by Coach Chris Mooney — who agreed to a 10-year contract extension this spring — the Spiders posted a 29-8 record on the season.

Old Dominion finished the 2010-11 season 27-7 and lost to Butler, which ultimately advanced to the Final Four, in the first round of the NCAA tournament.

Hampton won the 2011 Mid-Eastern Athletic Conference crown and was the league’s representative in the NCAA tournament. The Pirates lost in the first round to Duke.

James Madison, which — along with George Mason, VCU and Old Dominion — competes in the Colonial Athletic Association, posted a 21-12 record last season and lost in the first round of the CBI tournament.