Dibrell was born in Kentucky and moved to Seguin, Texas, in 1857. He completed school in Seguin and left for college, graduating college in Virginia in 1879. He then returned to Seguin, was a school teacher for 10 months and took private law studies with Harry M. Wurzbach. Admitted to the bar in 1882, he then began his law practice. Then was 21st District State Senator from 1894 to 1902, and president pro tem of the Senate in 1897. Also served as an associate justice of the Texas supreme court 1911 to 1913.
