Sergeant Sean Judd, of West Coast police search and rescue, said weather conditions meant they were unable to get into the area. The Alpine Cliff Rescue Team flew in early this morning.
"It appears the man has slipped and tragically fallen to his death," he said.
Mr Jacomb's body was flown to Fox Glacier and the rest of the party to Franz Josef.
His sister Pam Jacomb, who lives in Christchurch, posted on Facebook yesterday about the death.
"This morning I am devastated to let my friends know that my sweet, compassionate, adventure loving wee brother has died in the mountains he loved, after a fall. This part of NZ is stunning. I don't know how I'm going to get through this year"
A cousin from the US, Carter Adams said: "The world lost a great man today . . . He will be greatly missed by everyone lucky enough to have known him. His family and friends are shocked and devastated. If there was anything that needed to be done, Eric was ready to do it. Through the years, he did the chores, tended the sick and infirm, and was a good friend to all. When he would come to visit his American cousins, we never wanted him to leave."
A friend, who Pam Jacomb said had known the family for more than 50 years, wrote: "I've known him since we were wee lads on Vashon, and had several visits with him in the last decade as he travelled to the northwest to ski and hike and reconnect with his Vashon roots. Such a big hearted, open minded, thoughtful fellow.
"His passion for the outdoors was inspiring to me, as was his way of keeping things simple while travelling and just getting out there and adventuring."
On a profile on the LIC site, Mr Jacomb said he lived on a lifestyle block.
He added: "I am passionate about the dairy industry, and it is important to me to contribute back to the industry by helping dairy farmers to improve their businesses."
He said he graduated from Lincoln University in 1982.
Meanwhile, a 32-year-old Christchurch woman died while attempting to cross the Deception River near Otira on the West Coast today. She was part of a party of five trampers who were 3km up the valley and moving towards Goat Valley.
They were making their third crossing of the river when the woman became detached from the group and was swept downstream. She was found by her companions about 1km downstream. They carried out CPR and called emergency services, but she died at the scene.
Bruce Cameron, of the Otira Hotel, said he had called emergency services after being alerted to the incident by people from the woman's party.
"Two trampers came running into our hotel and wanted to ring 111, so we spoke to emergency services and organised the ambulance and tried to get a helicopter," he said.
"They said two doctors were up there tramping as well and they were doing CPR on her."