Friends and associates confirmed the body found at Watsons Bay in Sydney's east on Thursday to be that of the 59-year-old.
Melbourne gallerist D'Lan Davidson said Mr Klingender was "the architect of the market we have today,"
"He leaves behind a huge vacuum for Indigenous art in this country and around the world," he said in a statement on Friday.
Sydney gallerist Michael Reid said the art community had received the news with "profound sadness".
"The death of Tim Klingender was an unimaginable and devastating loss to his family and indeed the Australian art-world," he said.
"Tim was quick to laugh. First in on adventure and always up for a chat ... (he) had ability, warmth, and presence, in spades."
Friends said the art dealer had gone out on a boat for a fishing expedition early on Thursday morning.
The Marine Area Command initially responded to reports of boating debris floating in the water off Watsons Bay about 10.20am on Thursday.
Officers recovered the body of a man in the water of the debris field, police said in a statement on Friday.
Investigators are being assisted by PolAir and Rescue Squad to search for a second man, 51, who was believed to have also been in the vessel.
Mr Klingender was employed as the international director of Sotheby's between 1998 and 2009.
He founded Sotheby's Aboriginal art department in 1996, touring works internationally before their auction in Australia.
