"The Herenga Waka—Victoria University of Wellington received the news of Jack's death with great sadness," said Sport and Recreation Associate Director Karl Whalen.
"Jack was a loved and respected member of the team at Wellington University Recreation. What he meant to the team he worked in has become even more evident over the past few days.
"Our thoughts are with Jack's family, friends and colleagues at this difficult time."
Skellett is also being remembered by his former football club.
He played for Tauranga City AFC over several years, including for the under 19s team at the national championships, Chairman Brendon McHugh told the Herald.
💙 More sad news after confirmation that former blue, Jack Skellett was the missing kayaker found in Wellington...
"More sad news after confirmation that former blue Jack Skellett was the missing kayaker found in Wellington yesterday," the club wrote in a tribute posted to Facebook today.
"Jack played across a few teams, pictured here with one of our U19 squad's in Napier. Our thoughts go out to Karen & Adam."
McHugh said Skellett was "very liked and very popular".
Skellett went on to play football for Victoria University of Wellington Association Football Club.
"Jack joined us at the start of 2020, having previously played for Otago University and Tauranga City before that," the club said in a statement.
"Jack was a talented footballer who was well-liked and respected by his teammates and team management. He was a leader on and off the field and captained his team several times this season.
"He was friendly and approachable and was always willing to help when the club needed to deal with him in his work capacity as well. He will be sorely missed by his teammates and the wider club."
The search
Skellett set off from Petone beach on Monday morning and it's believed his intentions were to kayak around Matiu-Somes Island and back to Petone Beach.
Skellett's car was found in the carpark next to Petone Wharf.
Police and Coastguard began a search on Tuesday with the help of friends and family, focusing on the area between Days Bay and Baring Head.
Police said there was a likely sighting of him kayaking around the south end of Matiu-Somes Island between 1 and 2pm on Monday afternoon, reported by a boatie.
A blue kayak without the paddle, believed to be Skellett's, was recovered by search teams on the Pencarrow coastline, just north of Hinds Point, on Tuesday.
"Police's thoughts and deepest sympathies go out to his family, who have requested privacy at this difficult time," police said.