Monken, 46, coached Georgia Southern from 2010-13, building a 38-16 record. The Eagles were 7-4 this past season, they first in which Mon ken didn't have at least 10 wins.
Monken had taken Georgia Southern to the NCAA Football Championship Subdivision semifinals his first three years at the school.
"We want a successful head coach who understands the challenges of working at a service academy, one who could help us win immediately and one who understands the importance of West Point's mission. We found that in Jeff," said Army Director of Intercollegiate Athletics Boo Corrigan.
Monken replaces Rich Ellerson, who was fired last week after the Black Knights lost to archrival Navy for a fifth consecutive season with Ellerson as coach and 12th straight time overall. Ellerson was 20-41 over five seasons at Army.
Monken knows the Army-Navy rivalry well as he was an assistant at Navy from 2002-07.
"I am thrilled to accept the head coaching position at West Point," Monken said. "Not only is the United States Military Academy one of the most prestigious academic institutions in the world, it boasts one of the nation's richest, most historic traditions in all of college football.
"I am anxious to get started ... meet our players, put our coaching staff in place and begin preparations for the 2014 football season."
Teacher apologizes for showing sexual image of herself in class
Susan Sarandon 'very excited' about daughter's pregnancy