Conor Connolly told The New Zealand Herald he'd last caught up with Day in January for a coffee in Fulham, London.
"Joe was my best friend, we'd been best friends since intermediate school," he said.
"Disbelief and overwhelming sadness is how I'd describe my feelings."
Connolly said police were continuing to investigate the case and were reviewing CCTV footage in the area.
A Givealittle page has also been set up to bring Day's body to New Zealand.
The page was created by a close friend, Hayley Cashmore, to support Day and fiancée Kelsey Mulcahy's families and "costs related to bringing him home to rest in Aotearoa, New Zealand".
By early afternoon on Wednesday, the page had already raised $45,000.
Jaimee Lupton, co-founder of Monday Haircare, and Nick Mowbray, co-founder of the Zuru toy company, donated $3000.
Avon and Somerset police said a man's body was found in Avon Gorge, Bristol, late last night (NZT).
"While formal identification has not yet taken place, we have updated the family of missing 31-year-old Joseph Day," police said.
"Our hearts go out to them and we thank them for their patience while inquiries into the circumstances of death continue."
Day formerly worked at TVNZ as a cameraman.
A spokesperson for TVNZ said Day was a much-loved member of the broadcaster's whānau.
"He was an immensely talented man, full of warmth and kindness. We are devastated by this news. Our thoughts are with his family during this terrible time. We will be respecting their right to privacy and will not be commenting further," the company said.
TVNZ Sunday correspondent Mark Crysell also wrote on Twitter that Day, alongside his dad Pete, was a valued team member.
"His beautiful eye and deep soul became pictures that lifted our stories to another level," said Crysell.
Journalist Jehan Casinader thanked Day for sharing his talent in the industry.
"Whether it was the Christchurch terror attack, a trip to Hollywood... or a schoolboy rugby game in Palmy, you always delivered," he wrote to Twitter.
Andrew Macfarlane, who is based in Australia, said Day would be missed.
"Joe was a brilliantly talented camera operator, and had a real eye for things," he tweeted.
"He had a unique way of getting people to talk with ease in front of the camera, in a situation that can feel absolutely bizarre. A testament to how friendly he was to people."
TVNZ's Europe correspondent Daniel Faitaua said he was thinking of Day's family, friends and colleagues "at this very sad time".
Day's fiancee Kelsey Mulcahy earlier told the Herald she was frustrated that police initially deemed Day's disappearance as low risk and would not track his phone.
Day went missing on Saturday night (local time) from the couple's flat in the Bristol suburb of Clifton.
Mulcahy stopped hearing from Day around 9.30pm that night and raised the alarm when she returned home from London the next day to find he wasn't there.
Mulcahy, family and friends took to media and social media to appeal for help finding him.
