Police say the body found on Takapuna Beach yesterday was that of 26-year-old Stephen Kapeli, who was reported missing from Takapuna on Wednesday April 5.
Stephen's family say they are "heartbroken and devastated by the loss".
"He was such a loving, warm and gentle soul and he meant the world to us," they said in a statement released by police.
"Life has been full of many challenges for Stephen after being diagnosed with Bipolar Affective Disorder and we are in admiration of how he overcame many of the situations he was faced with. He touched the hearts of all who knew him.
"Stephen was an intelligent, warm, funny and empathetic soul with a gentle and caring nature. He had four passions - music, swimming, sport and gaming. He loved to play indoor netball and soccer and felt great enjoyment from spending time with his friends and family and being part of a team. But his true love was music and he found great comfort in music and being in, and near the water.
"We have so many wonderful and special memories of Stephen and he will leave an irreplaceable hole in our hearts.
"We would like to thank the police for their support and advice to our family over this incredibly difficult time. We'd also like to thank He Puna Waiora for the support they offered Stephen.
"There are no words to express how much we will miss our boy - Stephen will remain in our hearts forever."
Stephen was being treated in North Shore Hospital's mental health unit and disappeared while out on "approved unescorted leave".
He left the hospital's in-patient unit late last Wednesday afternoon and did not return at the time he told staff he'd be back by, Waitemata DHB's acting director of mental health Dr Mike Ang said last week.
He was last seen walking near Lake Pupuke in Takapuna about 4pm.
Staff at the hospital reported his disappearance to police shortly after he failed to return at the agreed time.
A relative told the Herald last week that Kapeli was expected to return from his walk about 5pm but did not.
Concerned family members contacted all his friends but no one had seen or heard from him, the relative said.
Police have referred the matter to the coroner.