The head of the Croatian Mountain Rescue Service, Prizmic Vincent, said a team of about 20 people searched for the couple in the rain for several hours.
Mr Branson was born in New Zealand but later moved to Australia, where he had been living in Melbourne for several years. He lists Katikati as his hometown on his Facebook page and is a former pupil of Katikati College.
He was a member of the Harlequin Rugby Club, in Melbourne, where he was considered a "great mate" and popular teammate, club chairman Brock Parker said.
"Yannick was a passionate Quins member from when he first arrived in 2008 and played in the club's second-grade premiership that year," Mr Parker said.
"He continued to play for the next three years primarily in second grade, but he did make a number of first-grade appearances."
Mr Parker said Mr Branson's love of rock climbing was well known within the club.
"He's been a passionate supporter from the sidelines and had forged many strong friendships at the club. He will be sorely missed by all on the sidelines."
Croatian authorities waited until yesterday to retrieve Mr Branson's body, as the cliff was too difficult to get to in the dark.
Ilinac Rock is popular with climbers and the area is also known for extreme sports, such as rafting and canyoning.
