Given final approval 20-10 on Wednesday, the bill brings ride-hailing companies under Texas regulatory control and imposes fees.
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The bill previously cleared the House, which included Tea Party-backed language defining "sex" as the "physical condition of being male or female." That's a reference to the Legislature's contentious "bathroom bill," which is separate legislation regulating transgender Texans' public restroom use.
The Senate preserved that language. Sponsoring Sen. Charles Schwertner, said, "it's stating the obvious."
The bill requires annual background checks, but not fingerprinting.
Houston and Austin are among the cities that currently require fingerprinting and background checks. Lyft pulled out of Houston a few years ago, while both Lyft and Uber left Austin because of the fingerprint requirement.
Once Gov. Abbott signs the bill into law, it's expected that Uber and Lyft will resume service in a number of Texas cities where they used to operate.
Lyft, which currently does not operate in Houston, called the legislation a "tremendous step forward" and said it will "create safer roads and expand reliable, affordable rides for Texans."
Houston city leaders have long maintained that fingerprint background checks are more accurate than internet-based background checks used by Uber and Lyft.
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The Associated Press contributed to this report.