The coin flip determined the 19th and 20th draft positions in the first round. The Falcons and Texans each finished 9-7 in 2009.
The coin flip was held at the NFL combine in Indianapolis.
It was the second coin toss won by Falcons general manager Thomas Dimitroff. The team drafted quarterback Matt Ryan after winning the No. 3 pick in a coin toss in 2008.
The Falcons have posted back-to-back winning records for the first time in franchise history.