The filing is required of candidates planning to run for state office, but it was unclear which office Bush might seek, if any.
Bush has not commented on the filing. The 36-year-old said in September that his goal was to run for office and acknowledged that he had his eyes on several statewide offices.
Raised in Florida, Bush decided to settle in Texas, home to his uncle and his grandfather, former President George H.W. Bush. He runs a consulting firm and has been active in Republican Party outreach to college students. He's also the co-founder of Hispanic Republicans of Texas, a group that seeks to elect Hispanic candidates.
Bush has served in the Navy and was deployed to Afghanistan for six months. For security purposes, he was given a different name while he was there - not even those he was serving alongside knew he was a Bush.
The Associated Press contributed to this report.