Dr. Ed D. "Tad" Barham must be confirmed by the Senate. Bryant nominated him to serve through June 30, 2017.
Bryant's announcement comes six days after Lt. Gov. Tate Reeves scuttled the nomination of Dr. Carl Reddix, a Jackson OB-GYN, to the board that sets state health policies.
Reeves' spokeswoman said the lieutenant governor had concerns about Reddix's connection to Mississippi's only abortion clinic. Reddix said he doesn't do abortions at the clinic but helps if patients have complications.
Reddix had served since last July, when he was chosen by then-Gov. Haley Barbour. Barbour submitted Reddix's nomination to the Senate on Jan. 3, a week before ending his second term as governor.