The approval comes after the state House passed it on Wednesday, US media reported.
The measure goes to Governor Greg Abbott, like Trump a Republican, to be signed into law amid a nationwide redistricting battle.
State senator Carol Alvarado, a Democrat, said on social media on Friday that she planned to delay the measure by speaking continuously about it in the legislature, a move known as a filibuster.
But a rare procedural motion by Senate Republicans just after midnight on Saturday ended the debate and killed the filibuster, moving the chamber straight to the final vote, the Texas Tribune reported.
The Senate adopted the bill on a party-line vote, 18 to 11, after more than eight hours of debate, the report said.
Republicans have acknowledged they believe winning more congressional seats in Texas will help the party maintain its slim majority in the US House of Representatives in the 2026 midterm elections, despite polls showing headwinds for the party.
More states controlled by Republicans are considering similar action.
California and other states where Democrats hold power vow to counter such moves.
The California legislature on Thursday approved a redistricting plan aimed at giving Democrats five more congressional seats - a move that must be approved by voters in November.
The Texas plan does not need voter approval, but Democrats have indicated they will challenge it in court.
The Texas bill was delayed for two weeks after more than 50 Democratic state House members staged a walkout that denied Republicans the legislative quorum needed. They have returned.
During debate on Friday, some lawmakers echoed criticism that Democrats raised in the House, that the new Texas map violates federal law by diluting Hispanic and Black voting power and discriminating on the basis of race.
Senator Royce West, a Democrat, predicted the new map would reduce the number of African Americans representing Texas in Washington from four to two.
"I call that retrogression," West said.
Texas senator Phil King, a Republican who sponsored the bill, said repeatedly he had not considered race and lawyers had assured him the bill met all legal requirements.
"From my perspective, why would I use racial data?" he told his fellow senators.
"Voting history is just much more accurate and is well established as a legal way to draw maps."
Most Americans believe redrawing congressional lines for the sake of maximising political gain, known as gerrymandering, is bad for democracy, a Reuters/Ipsos poll found this week.
