Texas Penal Code section 46.04 makes it illegal for someone who was convicted of a felony to possess a firearm before five years have passed since the completion of their sentence, parole, or probation. Once the 5-year period has passed, they can only possess a firearm at their home:
Sec. 46.04. UNLAWFUL POSSESSION OF FIREARM. (a) A person who has been convicted of a felony commits an offense if he possesses a firearm:
(1) after conviction and before the fifth anniversary of the person's release from confinement following conviction of the felony or the person's release from supervision under community supervision, parole, or mandatory supervision, whichever date is later; or
(2) after the period described by Subdivision (1), at any location other than the premises at which the person lives.
Federal law, on the other hand, is stricter and does not mention any kind of waiting period nor does it mention felonies. Instead, this law is aimed at anyone who has been convicted of a crime punishable by imprisonment for a term longer than a year. See 18 U.S. Code 922(g):
(g) It shall be unlawful for any person -
(1) who has been convicted in any court of, a crime punishable by imprisonment for a term exceeding one year;
to ship or transport in interstate or foreign commerce, or possess in or affecting commerce, any firearm or ammunition; or to receive any firearm or ammunition which has been shipped or transported in interstate or foreign commerce.
What qualifies as a firearm? It's important to review the legal definitions of the terms used in the law to understand when and how they apply. For example, some antique firearms are exempt from both the state and federal legal definitions of a firearm. See: Can someone who has been convicted of a felony own a black powder gun or a muzzleloader?
Because both state and federal law seem to be in conflict, it is difficult to provide a simple answer to this question. Other factors also come into play. For example, see: Can I own a gun if my spouse, partner, or someone I live with was convicted of a felony?
Interpreting and applying these laws to your particular situation requires the assistance of an attorney. Our librarians are not able to provide legal advice nor can we advise you on whether your situation complies with the law.