Rigby, 54, known as Kasha, died on Tuesday at Brezovica mountain resort in Kosovo, Magnis Wofe Murray said in a message response on Facebook.
Mr Murray said on Saturday: “We were to be married in September. Now I’m widowed and devastated.”
The resort’s official account posted on Instagram a picture of rescuers on a snowy hillside near to a foil blanket, and pulling a stretcher, saying its ski center rescue team “pulled out the victim from very dangerous part of hill when she tragically lost her life, even though they were in danger for their own life.”
It did not specify if it was Ms Rigby.
Rigby was a telemark, big mountain and expedition skier, covering first descents of some of the world’s most revered peaks and had appeared in several films and on a US reality TV show.
Considered one of the best female telemark skiers in the world, she was skiing out of the tourist lanes when an avalanche hit her, police said.
She died despite receiving immediate CPR from Mr Murray and later medical assistance.
Rigby was swept into a pine tree by a small avalanche in the “Eagle’s Nest” area, which is known for its avalanche risks, after dropping in at the top of the run, search and rescue staff said.
She was in Brezovica, 50 miles south of the Kosovo capital, Pristina, with the Tour de Piste, a project made up of expert skiers to navigate uncharted ski runs at popular locations.
