They were gunned down in the St. Barbs area last night.
Reports say the men were liming at Blundell Alley at around 8:30 when a vehicle drove up to them.
It is said the occupants opened fire.
Mr. Moore, Mr. Joseph and another man identified as Jermaine King were hit.
Mr. Joseph was pronounced dead at the scene.
Mr. Moore and Mr. King were taken to hospital where Mr. Moore died a short while later.
Mr. King remains warded in a stable condition.
Mr. Moore was 31-years-old and lived at Red Hill in Morvant.
Mr. Joseph was 31-years-old and lived at Upper St. Barbs and was said to be the leader of the St. Barbs branch of the Rasta City gang.
Police believe the killings were gang related as a volley of gunshots rang out in St. Barbs on Tuesday night.
Yesterday Police Commissioner Gary Griffith said warring factions of the Rasta City and Muslim gangs were firing shots at each other.
He said the issue stemmed from a box drain state contract.
He pointed fingers at governments past and present saying the politicians have been fueling crime in awarding millions of dollars in state contracts to gang leaders.