Chief David Brown said the suspect told authorities he was James Boulware and blamed police for having lost custody of his son and for “accusing him of being a terrorist”.
But authorities declined to officially identify the man until a medical examiner verified it.
A police sniper shot and killed the man in his van early on Saturday after, according to Mr Brown, the department felt he still posed enough of a threat.
The suspect had told police negotiators he had explosives in the van.
“When the negotiation was on, he became increasingly angry and threatening, such that we were not only concerned with our officers there trying to contain the scene being shot by him at a moment’s notice, but also people nearby,” Mr Brown added. Officers also found the man had planted pipe bombs outside police headquarters.
Police questioned Boulware’s father, also named James, later on Saturday.
Authorities said the shooting “miraculously” left no one else dead or injured. Among the areas damaged inside were the front desk which the worker on duty had just left to get a soft drink.
The suspect also fired on officers who drove up to confront him, riddling at least one squad car with bullets but not actually hitting anyone. Mobile phone video shot from a nearby balcony or roof showed the suspect’s dark-colored van ram a squad car as gunshots rang out.
At one point the man got out of his van and walked toward the entrance to the building firing his gun, but he turned around again, according to Dallas Police Major Jeff Cotner.
Police would not say why he retreated.
The van then fled, eventually stopping in a restaurant parking lot in the suburb of Hutchins, where the standoff ensued until the police sniper shot and killed the man.
Investigators found a package of pipe bombs in the parking lot at police headquarters and at least two more pipe bombs in the van, police said.
Wary that the van may have been rigged with explosives, police used a camera-equipped robot to inspect it rather than have officers approach it immediately. Because of this it took several hours to confirm the suspect was dead.
After Boulware was confirmed dead, the van erupted in flames while the authorities were detonating the suspected ordnance inside.
Boulware’s father said his son had strong feelings against law enforcement after he lost custody of his son, now 12 or 13 years old. Boulware spent several hours on Friday at his father’s home in Carrollton, a Dallas suburb.
His father said he talked about how well his recently purchased van drove.
But he also discussed a widely publicised video of a police officer in McKinney, Texas, pushing a black teenage girl to the ground and brandishing his gun at other teens.
Boulware’s father last spoke with Boulware by phone about three hours before Dallas police said the shooting began.
“Not being able to get a job and the legal system letting him down, he finally snapped,” James Boulware Sr said in a phone interview before police arrived to question him about his son.
“But I can’t say shooting at a police station is right in any way.”