RNZ understands the fishermen who died are Elwood Higgins, Damien Macpherson and Taina Sinoti.
Police said formal identification was under way.
The bodies of three fishermen have been taken to Gisborne hospital.
Whānau are waiting for the bodies to be released to them.
Police said that will happen once all relevant procedures have been completed, although it was unclear how long that would take.
A woman spoken to by RNZ, who is associated with one of the whānau, said they were broken.
But she said it was incredible the sea has brought the men home.
There has been an outpouring of tributes for the trio.
One man told RNZ all three men were good friends of his.
"Everyone in our region felt the storm the last few days but especially last night, with everyone's thoughts out at sea, praying that our men would be safe and returned. It's a tragedy for Tai Rāwhiti.
"We have lost some good buggers that are close with the rural, urban and coastal communities."
He said Gisborne was a small place, and everyone had been affected by the deaths of the three men who all had kids.
Harvey Marshall, a friend of Elwood Higgins, posted on Facebook that it had been a rough few days.
He told RNZ that he would never forget when he met Higgins.
"He's a big solid tower of a man and when I shook his hand, he had a funny squeaky voice that just never matched his presence - guess you have to look and see the funny stuff as well," he said.
Another friend said it was "absolutely devastating news to wake up to".
A cousin of Higgins said he had always looked up to him, and would always see him as the top man he was.
A farming leader said one of the three was a promising farmer.
Gisborne Federated Farmers president Charlie Reynolds said the tragedy has struck everyone in the community.
"I mean Gisborne is a small town, we all know at least one of them so the region is dealing emotionally with that.
"One of them was a very good young farmer who's left behind a very young family."
'Terrible day'
Tatapouri Fishing Club president Roger Faber was also out fishing on Monday and spoke to the missing fishers.
He said they were lured by some nice blue fin tuna, which was caught off Gisborne over the weekend, and a weather forecast that was meant to improve.
"We all communicated with each other as we went out and talked about our plans for the day.
"Unfortunately the weather was nothing like forecast, we expected it to get better, it didn't get better, it got worse," Faber told Morning Report.
He said when he pulled back at 11am because of the weather, they tried to contact the missing boat but could not.
"At the time, we didn't think too much of it, we thought 'oh well, hopefully they've just decided to go in earlier too'.
"But then when we returned to the boat ramp and saw that their trailer was still there, that's when our concerns rose and we sounded the alarm."
Hearing the bodies had been found, Faber said it was a "terrible day".
The men, particularly the skipper, were experienced and well-respected club members, he said.
"The whole community is suffering ... and whānau and friends will be really suffering."
Rescuers went to their limits
Maritime New Zealand Rescue Coordination Centre general manager Justin Allan said rescuers went to their limits trying to find the three fishers.
The search and rescue operation was difficult and complex, he said.
"Weather conditions in the area were severe ... Responders from the region, as well as rescue aircraft sourced from across the North Island had to battle atrocious conditions; including swells of up to and at times more than six metres, 50 knot winds and low visibility, showing how determined they were to reach the men in the water."
The conditions were just too severe, Allan said.
He extended his thoughts to the families and thanked everyone involved in the search efforts.
Community in mourning
Gisborne mayor Rehette Stoltz told Morning Report the news the bodies had been found was heartbreaking.
"Our community is in mourning."
She said her love and thoughts were with the families.
"Everyone is waking up to this news and our community is right behind them.
"We have put a call out there just to ask everyone give these families some space and let them bring their men home, and then when they are ready, as a community, we can lean in and look after them."
Stoltz said the region was experiencing some of the worst weather it had seen, which made the search difficult.
There had been an outpouring of grief this morning and a number of beautiful tributes on social media, she said.
Givealittle page gains traction
A Givealittle page for one of the Gisborne fishermen has recieved nearly $40,000 in three hours.
Damien Macpherson's close friends set up the page to help his wife, Vivienne Macpherson, and his children with the unexpected funeral costs.
They wrote that Damien, known as 'Damo', left behind a "devastated" young family.
"Damien Macpherson has tragically lost his life at Sea. A ray of light and love and laughter has been taken too soon."
There have been nearly 300 donations made by about 3pm.
"Such an incredibly sad loss to such a wonderful husband, father and friend," one donor wrote.
"An absolute tragedy. A beautiful soul taken far too soon," another wrote
The search
The search and rescue operation was suspended at 7pm Tuesday and had been due to resume today.
The boat carrying the three missing fishers was reported overdue on Monday afternoon.
The bulk carrier ship - the African Tiger - spotted two men in rough seas off Māhia Peninsula on Tuesday but could not reach them. Those on board threw life rings and flotsam into the water.
The Defence Force's P8 Poseidon also dropped a life raft in the same area.
Eastland Helicopter Rescue Trust chairperson Patrick Willock said searchers looking for the missing crew in horrendous conditions yesterday were nothing short of heroic.
A helicopter from the trust had been helping with the search.
