The veteran musician died on Monday in the US with his wife Suzanne and their eight sons at his bedside in Utah.
The family released a statement praising the pop legend's attitude in the years he spent suffering health issues following his diagnosis with MS in 1987.
"His positive outlook was an inspiration to many, and he donated much of his time speaking at MS events, encouraging individuals like himself on how to mentally and physically deal with the advancement and treatment of the disease," the statement said.
Osmond's cause of death has not been revealed.
The musician rose to fame as a child in the late 1950s after appearing on The Andy Williams Show in 1958 alongside his younger brothers Wayne, Merrill and Jay singing as a barbershop quartet when he was just 12 years old.
The group was joined by two more brothers, Donny and Jimmy, and they became The Osmonds.
The family band went on to find huge success in the 1970s, scoring hits with tracks including Love Me For A Reason and Down By The Lazy River.
Osmond became a keen songwriter, penning hits such as One Bad Apple and Crazy Horses.
Some of the group's members later went on to carve out solo careers including Donny, who also performed with sister Marie.
Alan Osmond left the band in 2007 and later launched a Fourth of July celebration event called the Stadium of Fire in Provo, Utah, with his brother Merrill, and co-founded a charity for orphans, the OneHeart Foundation.
Osmond published his memoir One Way Ticket in 2024.
During his life, he reflected on his MS diagnosis and shared his belief that the condition was given to him by God as a test.
"I was on stage and couldn't raise my right hand. I trusted my Heavenly Father. You have to have opposition in life - this was my test," he said.
Osmond married Suzanne Pinegar in 1974 and they went on to welcome eight sons. He is survived by Suzanne and their boys as well as 30 grandchildren and five great-grandchildren.
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