The bill was approved 19-11 along party lines Friday after a debate that drew thousands of supporters and opponents to the capitol, the Fort Worth (Texas) Star-Telegram reported Saturday.
Gov. Rick Perry, who had called the special session for which the bill was the only agenda item, is expected to sign the bill into law.
The regulations could force most abortion clinics in the state to close, opponents say.
During 8 hours of debate that ended just before midnight Friday, Democrats offered 20 amendments. All of them were rejected, including one that would have allowed abortion for pregnancies resulting from rape.
Democratic Senators had conceded defeat before the debate began, but offered the amendments to lay the foundation for a legal challenge.
State Sen. Wendy Davis, whose 11-hour filibuster thwarted action on the bill on the last day of a previous legislative session, said Friday night "this is something we should take our time with," charging Republicans had rammed the bill through for political reasons.
A line of people who wanted a chance for a seat in the Senate gallery began forming before dawn.
Department of Public Safety officers confiscated a variety of items that could be thrown at legislators, including feminine hygiene products and a jar suspected of containing urine. Officers stopped confiscating tampons after the practice became a subject of public ridicule.
Abortions after 20 weeks would be banned under the bill and abortion clinics would be held to the same standards as hospital surgical centers, The New York Times reported.
Many doctors opposed the bill, including leaders of the American Congress of Obstetricians and Gynecologists, which had run advertisements telling legislators to "Get out of our exam rooms."
Notable deaths of 2014 [PHOTOS]