Both the House of Representatives and the Senate approved the bill and sent it to Governor Rick Perry. He has indicated he will wait for a ruling by the U.S. Supreme Court before deciding whether to sign the bill into law.
The nation´s highest court is considering the case of Texas death row inmate John Paul Penry, 44, who was convicted of a 1979 murder but is said to have a mental age of 7.
Earlier this month the Texas legislature rejected a bill, backed by Perry, that would have allowed juries in capital murder cases to pass a sentence of life in prison without parole.
Now, Texas juries must choose between death or life imprisonment with the possibility of parole after 40 years. Supporters of the defeated bill argued the third option was needed because juries were likely to choose the death penalty for fear a convicted killer might be freed and kill again.