The chamber voted 72-22 to pass the measure sponsored by Republican Rep. Jeremy Faison of Cosby after rejecting a series of Democratic proposals to maintain business owners' rights to ban weapons on their property and to create exceptions for schools and colleges.
House Speaker Beth Harwell told Republican colleagues before the vote that members of the business community are "holding their nose" over property rights concerns about the measure.
Republican Gov. Bill Haslam has raised concerns about the measure in the past, but has not said whether he will sign the bill into law.
The controversial plan already passed a full Tennessee Senate vote on Feb. 11.
The Senate approved the bill 28-5 after rejecting Democratic efforts to add potential exclusions for businesses.
"If they are denied to have that weapon, should they choose to have one in their automobile while at work, then they are denied the right for self protection to and from work," State Sen. Jack Johnson, R-Franklin, said last week when the measure passed the Senate Judiciary Committee.
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