Chandra Bahadur Dangi, who is also known as Prince Chandra, died in hospital in Pago Pago last week, aged 75.
The Guinness Book of World Records says Mr Dangi was the shortest man on earth at 54.6 centimetres in height.
The Nepalese national was in the territory as part of Bruno's Magic Circus.
The ringmaster, Tupai Bruno Loyale, says Mr Dangi was a simple man with a big heart.
"He was always cheerful, always so kind and he loved life. I will never ever forget, as I sit in my kitchen tent, I hear his little voice laughing and talking in his native language with my performers."
Mr Dangi's body will be returned to his family in Nepal for cremation.