Sean Hercules, 39, was approached in an aparthotel near Malaga after Spanish police said he was spotted fleeing a car crash with a weapon.
Witnesses saw him leave the crash site in the upmarket party resort of Puerto Banus, near Marbella, on Monday morning before he was traced to a hotel in the town of Estepona, around 20 minutes' drive away.
He opened fire on officers after they confronted him and was then killed in the shoot-out, Spanish national police in Malaga said.
Two firearms and four cartridges were found next to his body.
Hercules had a history of drug trafficking and weapons possession, the statement added.
He has links to Osmondthorpe, Harehills and Holbeck.
Hercules was convicted of shooting a man with a sawn-off shotgun outside the Warehouse nightclub in Leeds back in 2006, when he was 27. The attack happened during a night of 'Wild West' violence in the city centre the previous year.
He was also jailed for his role in a robbery at a post office in Gipton in 2001.
Hercules had originally faced a charge of attempted murder in relation to the Warehouse shooting, which left victim Nathaniel Stapleton with more than 250 gunshot pellets in his body.
However, his guilty pleas to wounding with intent to cause grievous bodily harm, possessing a firearm with intent to endanger life and possessing a prohibited weapon were accepted at his trial.
Judge James Stewart QC told him: “The citizens of Leeds who come out of nightclubs in the early hours of the morning are entitled to believe they live in a civilised society, not the Wild West.”
A Foreign and Commonwealth Office spokesman said: "Our staff are in contact with the family of a British man following his death in Spain, and have offered them support and advice on bereavement abroad."
A judicial investigation into the fatal shooting has been ordered, Spanish police said.