"Over the past few days I've been privileged to hear stories about this young soldier - a good southern lad from Gore who was a determined and capable soldier with a passion for mountaineering.
"Morgan was Aumangea Programme qualified, and had a promising career ahead of him.
"Morgan's loss will be keenly felt by his family, comrades and mates. My thoughts and prayers are with them as they come to terms with their loss. His service to New Zealand will not be forgotten."
A post on the First Battalion's Facebook page described Fraser as a "passionate" member of the platoon who would be sorely missed.
Other friends and comrades also paid their respects online.
"Totally shattered. Morgan Fraser it was too soon. Thank you for being a good mate and always seeing the good in everything. All the boys respected you bro you were a lad. One of the best mates I had in the military. Onward miss you brother," one posted.
Another wrote: "My brother Morgan Fraser , I hope you are at peace. Until we meet again my bro. Onward ."
On Facebook sister Meredith Fraser wrote the family was "heartbroken".
"We're absolutely devastated to lose such an amazing son, brother, grandson, friend and all-round good sort.
"We take comfort in knowing that he was doing something he loved.
"Thank you to everyone for their kind messages and support. A special thanks to the Police, Army, and Search and Rescue teams for helping to find Morgan and bring him off the mountain.
"We're working through service arrangements and will advise when we have these confirmed.
"Words can't describe how we feel right now and how much we miss Morgan. It's hard to summarise his life and all his good qualities. He's going to leave a huge hole in our family. We love you Morgan. Xx"
About 3.50pm on Wednesday police were alerted that Fraser had failed to return from a climbing trip the day before. He was expected back on Tuesday evening.
Police and search and rescue teams searching the mountain found his body just after midnight.