The state College Board made the decision Friday during a meeting on the Columbus campus.
Higher Education Commissioner Hank Bounds cited Brigham's management and communication skills as contributing factors for her selection. Bounds described Brigham as business-savvy and with ties to MUW at a time when the struggling university needs her.
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.
The College Board committee is in the process of searching for a new president at MUW, which has an enrollment of 2,478 students.
MEC President Blake Wilson said Brigham brings a broad business background to the university, especially in terms of marketing MUW.
"Dr. Limbert has done an outstanding job of building the academics at MUW. Allegra can come in and put an emphasis on finances and marketing," Wilson said.
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 chair of the North Mississippi Industrial Development Association.
Brigham previously worked as MUW's director for public relations.
The MUW presidency is one of three that must be addressed by the College Board. The other two are at Alcorn State University and Jackson State University, where interim presidents have been named.
Read more in Saturday's NEMS Daily Journal.