The legislative package still must pass the House. One piece of the legislation would require voters to approve a constitutional amendment.
Williams said the rebates would also help low-income Texans.
"We're going to give the money back to those folks who overpaid," he said.
The vote fell along party lines. Democratic Sen. Kirk Watson of Austin criticized the plan as part of "pre-election gimmicks."
Sen. Eddie Lucio, D-Brownsville, said, "There are a lot of needy people who certainly depend on this fund and would hope we could continue it."