Austin Police chief Brian Manley said the 24-year-old male suspect, who has not been named, had been tracked him down to a hotel in Round Rock in the US state.
The suspect set off the explosive device inside his vehicle as a SWAT team approached.
One of the SWAT officers also shot at the vehicle and an officer was injured in the explosion.
Mr Manley said the motive behind the series of bombings, which killed two people, was unknown.
He also urged Texas residents to be “vigilant” for other possible explosives, adding: “We do not know where he has been in the past 24 hours”.
US president Donald Trump, who had earlier branded the Texas bomber a “sick individual”, praised law enforcement officials.
AUSTIN BOMBING SUSPECT IS DEAD. Great job by law enforcement and all concerned!
— Donald J. Trump (@realDonaldTrump) March 21, 2018
The Bureau of Alcohol, Tobacco, Firearms and Explosives had earlier confirmed it was at the scene “of the individual suspected in the package bomb murders” on the I-35 highway.
— ATF HQ (@ATFHQ) March 21, 2018
The suspect was identified in the last 24 hours after shipping an explosive device from a FedEx store in the Texas capital, the Austin Statesman said.
Authorities found store receipts showing suspicious transactions and obtained a search warrant for his Google search history which also showed suspicious behaviour, an official told the newspaper.
Police then used mobile phone technology to trace the suspect to a hotel in Williamson County and a chase ensued, according to reports.
A string of bombings over the past two weeks killed African-American men Anthony Stephan House, 39, and Draylen Mason, 17, and injured a number of other people.
Mr House died after a device exploded at his home in Austin in the first attack on 2 March.
Mr Mason was killed and his mother critically injured in a blast on 13 March after a package was left on his doorstep.
Hours later, a 75-year-old Hispanic woman was critically injured after another package exploded in Austin.
On Sunday, two men, aged 22 and 23, were seriously injured in an explosion involving a tripwire device.
In the early hours of Tuesday, a FedEx worker was hurt after a package bound for Austin containing nails and shrapnel blew up at a distribution centre in the San Antonio town of Schertz.
Later that day, another explosive package was intercepted before going off at a FedEx facility outside Austin airport.
US president Donald Trump branded the person behind the attacks a “very sick individual, or maybe individuals”.