Darren Brown, 21, from Southwell in Nottingham, was hit three times in the chest as he advanced on armed police, waving the weapon and shouting obscenities, Miami police said.
The incident happened at 9am local time outside an English-style pub called the Hungry Sailor in the Coconut Grove area of the city. A police spokes-man said Mr Brown had been refused entry the previous night "because he was too inebriated".
Two officers received a report that a man armed with a machete was trying to break into the pub and they confronted Mr Brown. According to police, Mr Brown began threatening the officers with the machete and then turned on motorists, causing several to abandon their cars and run away. When a third officer arrived, Mr Brown lunged at him, and the other two opened fire.
Mr Brown had been in the US on a 90-day visa since January 1994 and was described by police as "an illegal overstay".