The quake triggered a massive avalanche that swept through the base camp, killing at least 18 people and injuring more than 60.
At the time of the avalanche, the Hillary group was between the tiny village of Gorak Shep, which is about 4km down valley from the base camp, and the base camp itself. They returned to the Gorak Shep, and on Sunday proceeded down to Tengboche.
Mr Kay's brother, Geoff, told nzherald.co.nz today on behalf of the family: "We are devastated at this sudden loss of a much loved member of our family. Greg was a unique, kind and generous man who will be greatly missed.
"At this very difficult time, the family asks for privacy and time to grieve."
Greg Kay is survived by his wife, Sudy, two adult sons and one granddaughter, and both of the son's wives are expecting babies, which, Geoff Kay said, "is a great sadness for us that Greg won't see them".
Geoff Kay said the family was working with authorities in Nepal to make arrangements for the return of his brother's body to New Zealand.