Authorities on Wednesday had tentatively identified the body as Brian Reed, who jumped into the river after an encounter with a sheriff's deputy on Jan. 7.
An autopsy Thursday by the Jefferson Parish coroner's office confirmed his identity and found the preliminary cause of his death to be accidental drowning.
Ed Reed said in a news conference Wednesday that his brother was driving another brother's car on Jan. 7 and was suffering "mental issues" that day. The family reported the car as being driven without authorization to "basically slow my brother down and just bring him in, bring him home," Reed added.
"Unfortunately, he thought otherwise," Reed said of his brother. "There was nothing illegal going on or anything like that."
A deputy later spotted Brian Reed with the car, which had run out of gas. Champagne said the deputy had an "amicable" conversation with Reed and offered to help him get gas, but he declined. As the deputy started to leave, a call came over the radio that Reed was suspected of using the car without authorization.
When the deputy started to pat him down, Reed pulled away and started to "jog off," St. Charles Parish Sheriff Greg Champagne said. The deputy followed Reed and saw him run over a levee but didn't see him enter the water, about 30 miles northwest of New Orleans.
"For reasons that only Brian would know, he chose to go into the river," Champagne said.
The family has said investigators found Brian Reed's shoes and jacket, but there was no sign of him until earlier this week.
The body was first spotted Sunday, but search teams were impeded by river conditions. The current is swift as it winds toward the Gulf of Mexico, lodging debris against the levee and then pushing it back toward the channel. Boats searched the river, and sonar and divers were called in to help.
Champagne said the body was mired in a "jungle of debris," and for a time, he was uncertain it could be recovered.
"We're just hopeful the Reed family can have some peace now," he said.
Brian Reed is survived by a 2-year-old son.
"He was a loving kid," Ed Reed said of his brother. "He had a son who he cherished and loved. That was his reason for living."
"We are not immune from trials and tribulations that go on through life," Reed said.
Copyright 2011 by The Associated Press