The person who allegedly shot and killed a man outside a Hollywood nightclub has been arrested ... TMZ has learned.

Law enforcement sources tell TMZ ... Robert Earl Thomas III was hiding at a friend's house in Las Vegas when cops entered the premises last night and placed him under arrest for murder.  He surrendered without a struggle.

TMZ posted video of the shooter outside Empire nightclub when he aimed the gun and fired, killing one man and wounding another.  The video clearly shows the shooter and law enforcement tells us they got a number of tips from people who saw it and that led to Thomas' capture.

Thomas is 22 years old and lives in Los Angeles.

Thomas is currently being held in a Vegas jail and prosecutors plan to extradite him to California.

A man was shot dead outside a Hollywood nightclub early Sunday morning in the throes of a massive brawl ... and our photog captured it all.

Cops tell us ... It started inside Empire nightclub ... where several fights broke out between some women ... before it moved outside.

You see women in the video throwing punches, pulling hair, slapping etc.  

Within minutes the violence escalated into all out mayhem ... dozens more joined in -- men and women.

Suddenly ... a man in a grey sweatshirt pulls a gun ... takes aim -- and two shots are clearly heard.

Moments later, you see a man lying dead in the middle of the street -- and it appears the victim was the intended target.

Another man was also shot during the brawl.  He's in stable condition.

The shooter was not apprehended. The LAPD is looking for him.