The last independent elected Texas governor was Sam Houston in 1859.
"Not one but two viable independent candidates have made the ballot for the first time in nearly 150 years," Friedman, a musician and author, said in a statement. "This tells us what we've long suspected: the two-party system has failed our state."
Strayhorn, the state comptroller who bills herself as "one tough grandma," is the mother of former Bush administration press secretary Scott McClellan.
Both Strayhorn and Friedman turned in far more petition names by the May 11 deadline than the 45,540 required. Strayhorn submitted some 223,000 signatures and Friedman submitted 169,574.
Among other limitations, the signatures had to be from registered Texas voters who did not cast ballots in the Republican or Democratic primaries this spring.
The Texas Secretary of State's Office began making final checks of the signatures Monday after the petition names were entered into an electronic database.