The Texas Senate approved the bill Sunday, sending it to Republican Gov. Rick Perry, who was expected to sign it.
Republicans have said they could pick up as many as six additional seats in Texas' 32-member delegation, which is ruled 17-15 by Democrats. Democrats said the map would add seven Republicans.
After the vote Sunday, Republican Lt. Gov. David Dewhurst said the new plan better reflects voting trends in the state.
"I think this map will lend, will create, new members of Congress being elected in the 2004 elections," Dewhurst said.
Democrats have opposed every attempt by Republicans to pass a new plan, saying the current congressional boundaries drawn by a court in 2001 should remain in place.
Sen. Leticia Van de Putte, a Democrat, said the map was crafted with one objective in mind and "that was to increase the maximum number of Republican congressmen and women in the state of Texas."
"In doing so, it ripped apart communities of interest, it tore at the heart of rural Texas and it violated the voting rights millions of African-Americans and Hispanics," Van de Putte said.
Dewhurst said the map will "elect more minority members to Congress."
Although the bill was approved, Democrats twice held up the redistricting effort by staging boycotts of the Legislature.
House Democrats broke a quorum in their chamber, killing the redistricting effort, when they fled to Ardmore, Okla., in May. Senate Democrats held their own quorum bust when they fled to Albuquerque, N.M., for the full second special legislative session.
The Senate Democrats returned reluctantly after one of their group decided to go back to Texas.
Because the Legislature took so long to approve the plan, it also was forced to vote to push back the Texas primary election by one week to March 9 to allow for the new congressional districts to be incorporated on the ballot.
Although the legislative battle is over, Democrats have pledged to fight the new map in court.