A native of Kentucky, Delabar attended Central Hardin High School and Volunteer State Community College.

He was selected late in the 2003 MLB draft by the San Diego Padres and began his minor league career in 2004.

Delabar helped to implement an arm conditioning program for pitchers at the high school and found that his own pitching velocity improved significantly.

He started the 2004 season with the Arizona League Padres, going 3–4 with a 4.37 ERA before earning a promotion to the Single-A Short-Season Eugene Emeralds.

He played 2006 with the Single-A Fort Wayne TinCaps, then the Wizards, earning an 8–9 record with a 3.41 ERA in 27 starts with 118 strikeouts.

He started 2007 with Single-A Advanced Lake Elsinore Storm, but was demoted back to Fort Wayne after registering a 5.59 ERA out of the bullpen.

[3] He did not play professionally in 2010, working as a substitute teacher in his hometown of Elizabethtown, Kentucky at John Hardin High School.

He also played slow pitch softball, where he won the 2010 Louisville Invitational Tournament Miken Homerun Derby.

While introducing an arm conditioning program to his high school players, Delabar's own fastball returned to the 92-97 mph range.

He was assigned to Single-A Advanced High Desert Mavericks before being promoted to the Double-A Jackson Generals and the Triple-A Tacoma Rainiers.

On July 30, 2013, while facing the Oakland Athletics, Delabar struck out all three batters in the eighth inning on nine total pitches.

[1] After opening the 2014 season with a 4.68 ERA and 16 walks through 25 innings of work, Delabar was optioned to the Triple-A Buffalo Bisons on June 17, 2014, to make room for Munenori Kawasaki.

[1] On January 15, 2016, Delabar and the Blue Jays avoided salary arbitration by agreeing to a one-year, $835,000 contract.

[24] On May 17, in a game against the Cleveland Indians, Delabar walked four consecutive batters with the bases loaded, allowing four runs to score.

On January 4, 2018, Delabar signed a minor league contract with the Texas Rangers with an invitation to spring training.