Frederick Steiner said the policy was not "appropriate" for higher education and "did not make logical sense".
Texas passed the legislation last year and it goes into effect in August.
Many higher education officials and students have objected to the law, with concerns it may discourage students from attending universities in Texas.
Supporters of the law argue it is "critical" to self-defence and upholding constitutional rights.
But for Frederick Steiner, dean of the Texas School of Architecture, guns should not be allowed on university grounds.
"I grew up believing there was an appropriate place for guns and it was not in a place of higher education and higher learning," he told Fox News.
"I thought I would be responsible for enforcing a law I don't believe in," said Mr Steiner, who has been at the school since 2001. He says he plans to return to the University of Pennsylvania, but not until the law is passed in August.
Greg Fenves, president of the University of Texas, has said he does not support guns on campus but he must enforce the law.
Mr Fenves said that the law would make it more difficult to keep faculty and students at the university.
Long-time dean Frederick Steiner agreed, saying it was "already part of the conversation when I was trying to recruit and retain graduate students."
Meanwhile, staff at the University of Houston have warned professors there to be careful discussing sensitive topics and drop them from the curriculum if they "sense anger" from students who may be armed.
According to the Houston Chronicle, they have been instructed to "not 'go there' if you sense anger; limit student access off hours; go to appointment-only office hours; only meet 'that student' in controlled circumstances".
According to the law, private universities are allowed to ban guns on campus.

Tom Dryden, from Earls Barton in Northamptonshire, described the news as "absolutely outstanding".
Lorna Clarke, from Oxford, took the the women's title. It's the second time she has entered the games.
Organisers said 190 competitors from countries including Russia, the USA and Japan took part in the event in Southwick, Northamptonshire.
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Since it began in 1965, the event has raised about Â£400,000 for blind and visually impaired charities.
Ms Clarke, a digital marketing manager said: "Its amazing.  The trick was skill, accuracy and a little bit of luck.  My colleagues will laugh but will be very impressed."
Mr Dryden, who is a Cub Scout assistant, said: "I never thought I'd win the first time I entered.  The cubs will be over the moon."
A new conker is used for every round. StJohn Burkett said preparations had been tough this year because of a shortage of decent conkers.
He said: "We collect a couple of thousand and we have to get the proper Championship-sized conkers. They're quite rare.
"We usually rely on two secret trees but even they haven't produced this year so we've had the whole committee out collecting."

The 28-year-old Croatia international will sign the deal, which has a £109m (125m euros) buyout clause, on Friday.
Rakitic - whose current contract runs until 2019 - has made 145 appearances for Barca since his 2014 move from Sevilla, scoring 23 goals.
He played in Barca's famous 6-1 comeback win against Paris St-Germain in the Champions League on Wednesday.
A dean at the University of Texas is stepping down over a new state law which will allow concealed handguns to be carried on university campuses.
[NEXT_CONCEPT]
A new king has been crowned World Conker Champion after taking part in the annual games for the first time.
[NEXT_CONCEPT]
Barcelona midfielder Ivan Rakitic has agreed a new contract, tying him to the Spanish champions until 2021.