Rescuers said Mr Branson fell from a height of about 50m. Ms Nykanen was rescued from the halfway mark - about 250m up. She was said to be in a state of shock.
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, 40km north of Tauranga, 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 and he had told teammates he was going to Europe on holiday, where he expected to do some climbing.
"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," Mr Parker said.
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.
