The trio - a Hendon man, 26, an Albert Park man, 20, and a man of no fixed address, 22 - were arrested today over the February assault, which left the victim with injuries including collapsed lungs, a broken jaw, a broken leg and other facial fractures.
Police said several items of jewellery were also stolen from the man during the assault, which had now been seized and would be forensically tested.
It was strongly suspected at the time that the assault was as a result of an internal conflict among the Finks, police said.
The three men - two of whom are Finks members and the other a Finks associate - have been charged with aggravated cause serious harm and aggravated robbery.
They will appear in the Adelaide Magistrates Court this afternoon.
Crime Gangs Task Force officer-in-charge Detective Superintendent John DeCandia said two other offenders were believed to be linked to the attack and police needed help to identify one of them.
"Gang violence will not be tolerated and we will take action to ensure that those responsible are arrested and made to account for their actions," he said.
"The investigation is ongoing and further arrests have not been ruled out."