Tibbs was the son of a psychology professor at New Orleans Baptist Theological Seminary and Tulane University. During his father's sabbatical in Germany, Italy and Switzerland in 1936-37, young Ted caught a glimpse of Adolf Hitler leading a youth parade in Bad Homberg.
Tibbs majored in piano performance at Furman University in Greenville, South Carolina and switched to organ after transferring to the Eastman School in Rochester, New York. He returned to Europe as a student in the 1950s, laboring under organist and composer Jean Langlais in Paris. He completed his graduate studies at the University of Michigan, then returned to Furman as an instructor before accepting a position at Samford in 1959. He assumed the role of organist at Southside Baptist on March 1, 1960. In addition he has served as organist for the Alabama Symphony Orchestra.
In the 1970s Tibbs studied organ construction and performance across Europe and England. He has designed numerous organ installations in the Birmingham area, including the pipe organs at Brierfield Presbyterian Church, Samford's Andrew Gerow Hodges Chapel, the BJCC Concert Hall, the Samford Memorial Pipe Organ at Southside Baptist, and one and in his own home in Altamont. He has also designed organs in Tennessee, Mississippi, Georgia and South Carolina.
In 1981 Tibbs took charge of the Birmingham Music Club, shepherding it out of bankruptcy over the next five years before handing the reigns to Penelope Cunningham in 1986. He also served as booking director for the Birmingham Chamber Music Society. He retired from teaching full time at Samford in 2002.
- Huebner, Michael (May 19, 2002) "Retirement for Tibbs means exiting classroom." Birmingham News
- Garrison, Greg (October 10, 2009) "A couple of classics: Southside Baptist's vintage organ at 40, organist Tibbs in 50th year at the keyboard." Birmingham News
- Huebner, Michael (September 20, 2010) "In memorium: H. Edward (Ted) Tibbs enriched the lives of students, arts patrons." Birmingham News