West Yorkshire Police said the 42-year-old was wounded after officers returned fire at around 5.30am today at an address in the Kirkheaton area of Huddersfield.
The man had been locked in an armed stand-off with police lasting from 10pm last night to 6am this morning.
During the incident, one officer was shot and others came under fire as they attempted to negotiate with the gunman.
A police spokesman said: "We regret that the incident at the house did not conclude peacefully as we had hoped and can confirm that the man taken to hospital from the address has now died. We are not in a position to name him at the moment."
The man opened fire on officers as they attempted to arrest him at around 10pm last night.
A male PC was hit by a bullet and suffered minor injuries when the man took aim from his doorstep.
The gunman then returned inside the property before continuing to fire at police.
Teams of armed officers cordoned off the area and surrounded the "isolated" address following the incident.
Reports this morning said a man had been captured by police after officers stormed the property, bringing an end to the siege.
He died after being rushed to hospital.
Eyewitnesses said a number of shots were heard after police entered the address, before the man was taken away from the scene in an ambulance.
A West Yorkshire Police spokesman said that incident had began when the man had gone to a nearby address looking for a second man and then making threats towards him.
When he saw the officers, he produced a handgun and opened fire, hitting one of them.
A cameraman at the scene said the suspected gunman appeared to be uninjured after officers stormed the house.
He said: "There were three loud bangs, possibly gunfire.
"Then the police started shouting and I heard them smashing glass as they went into the house. They were shouting at the gunman to show them his hands."
He added that paramedics were allowed into the building after half an hour and the man was removed in a wheelchair, rather than a stretcher.