Mr dos Santos, who was 24, was shot three times on Monday when he confronted the officer and another man.
He underwent four operations before dying in hospital on Tuesday afternoon.
Mr dos Santos gained prominence after knocking 11-time world champion surfer Kelly Slater out of an event in 2012. He was known as a daring tube rider who had won international surfing awards.
There are conflicting reports on why Mr dos Santos was attacked by the police officer.
A witness reportedly said that Mr dos Santos had asked the men to leave after spotting them using drugs and playing loud music on the beach outside his home, near the southern city of Florianopolis.
Other reports say he was shot while discussing a car they had parked at his property.
The officer who shot the un-armed surfer says he did so in self-defence.
He has been detained, but has not yet been charged