Born and raised in Athens, Georgia, Titus attended Cedar Shoals High School where he was active in the theatre program. He graduated from the University of Georgia with a BA in music. He has appeared in four Broadway musicals and is known for his high tenor voice. Burgess is openly gay. 
- For his role as Titus Andromedon, Burgess received two Primetime Emmy nominations in 2015 & 2016 for the "Outstanding Supporting Actor in a Comedy Series" category.
- Burgess was the first male actor ever to be cast in the role of The Witch in Into the Woods in a 2015 production by DreamCatcher Theatre which performed in Miami's Carnival Studio Theater at the Adrienne Arsht Center.
- In June 2016, Burgess reprised his role of "Sebastian the Crab" during the Hollywood Bowl concert event of The Little Mermaid.