Napier deputy mayor Faye White said Thompson lost his life in "tragic circumstances" and her thoughts were with his family and the community.
Napier councillor Rob Lutter said: "The local fishing community is very small and it's a very tight-knit group and I'm sure they'll be fully supporting the family of this man."
Hawkes Bay Seafoods company director Joe D'Esposito said he was awaiting further information. His brother Nino declined to comment.
Coastguard skipper and duty manager Neil Daykin was alerted at 3.40am to reports of a person lost overboard just off Napier.
A search was organised, involving police, a rescue helicopter, a Coastguard aeroplane and half a dozen private boats.
"There was a huge number of crew involved as well as members of the public in private vessels," Daykin said.
The Coastguard air patrol spotted Thompson's body in the water about 8.30am. Police said he had drifted about two nautical miles.
Eastern district police communications manager Kris McGehan said the case was being treated as an accidental drowning.