If passed as expected, the measure is likely to draw a legal challenge from critics who consider it a constitutional violation of the separation of church and state.
The Republican-controlled House gave its preliminary approval on Saturday, with a final vote expected in the next few days. That would send the bill to the desk of Republican Governor Greg Abbott, who has indicated he will sign it into law.
"The focus of this bill is to look at what is historically important to our nation educationally and judicially," said Republican state representative Candy Noble, a co-sponsor of the bill.
Two other states, Louisiana and Arkansas, have similar laws, but Louisiana's is on hold after a federal judge found that it was "unconstitutional on its face".
Those measures are among efforts, mainly in conservative-led states, to insert religion into public schools.
Texas lawmakers also have passed and sent to Abbott a measure that allows school districts to provide students and staff a daily voluntary period of prayer or time to read a religious text during school hours. Abbott is expected to sign it.
Supporters of the Ten Commandments in classrooms say they are part of the foundation of the United States' judicial and educational systems and should be displayed.
But critics, including some Christian and other faith leaders, say the Ten Commandments and prayer measures would infringe the religious freedom of others.
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