The state College Board made the decision Friday during a meeting on the Columbus campus.
MUW President Claudia Limbert announced in October that she would retire at the end of June when her current contract ends. She had been at MUW since April 2002.
Brigham earned her bachelor's and masters degrees from MUW. She was named to the post at 4-County in 2003 and has been with the electric cooperative for more than 20 years.
In February, Brigham was named to serve on the board of directors for the Memphis Branch of the Federal Reserve Bank of St. Louis.
Brigham also serves on the board of directors of the Mississippi Economic Council, as chairwoman of the Columbus-Lowndes Development LINK and vice chairman of the North Mississippi Industrial Development Association.