It is the first collegiate head coaching job for Brock, who was offensive coordinator at Rutgers last season.
Keeler was fired recently after his 11th season with the Blue Hens.
"Coach Keeler did a great job. I'm confident that we have the building blocks in place to win in 2013 and forward," Brock said.
Keeler had an 88-52 record at Delaware. The team was 5-6 in 2012.