"Danny has a huge family in the Army whom he always had brothers to share adventures with. We are blessed with the amazing support the Army has given us, making an impossible time a time of love, support, and space to grieve. Also our thanks to the Police and special mention to Detective Sergeant Glen Yule from Hastings Police.
"Danny was a loving, loveable, and respectful young man who gave to so many in so many different ways. We are feeling all the love that Danny had given to so many, which is now being returned to us and we are eternally grateful."
The Defence Force said Sapper Jordan's family asked for privacy while they come to terms with their loss and grieve for their loved one and asked these wishes to be respected.
They advised no other statement will be offered.
Detective Sergeant Jason Crowe said Mr Jordan was shot as he and his two friends were sitting on the Sparrowhawk bivouac walking track, taking a break from their tramp into their hunting area.
While most hunting accidents occurred in heavy bush or rugged terrain, this one was different in that it occurred in open bush on a DoC track used to access the Ruahine Range.
"The shooting is an example of what can happen when firearms safety rules are not followed and hunters don't identify their targets properly," Mr Crowe said.
Police are urging all hunters to exercise extreme caution when in the bush and not to get carried away by the start of the new hunting season.
"Don't let the excitement of the roar affect your ability to make the right safety decisions. As this case illustrates, a small mistake can have fatal consequences."
There are seven basic rules covered in the Firearms Safety Code that hunters should abide by, including identifying your target properly and handling firearms safely.
"We can't stress enough the importance of these rules and urge anyone using firearms to follow them to the letter," Mr Crowe said.