The sponsor of the bill that would have cut the benefits, Republican Rep. John Zerwas, said he has reached a deal easing them amid criticism that his original plan would hurt the state's heroes.
During two hours of debate Sunday, some House members opposed cutting veterans' benefits before Memorial Day. The vote eventually was delayed until evening.
Under the agreement, Zerwas said the House will only mandate that veterans be Texas residents for eight years before receiving free tuition, and study the program.
Its cost to Texas public universities has climbed from $24.7 million in fiscal year 2010 to $169 million last fiscal year.