More details of the finds are to be announced soon.
Until now only the bones of cave bears have been discovered.
The new finds are of 'world importance', according to one of Russia's leading experts on extinct Ice Age species.
Scientist Lena Grigorieva said of the island discovery of the adult beast: 'Today this is the first and only find of its kind - a whole bear carcass with soft tissues.
'It is completely preserved, with all internal organs in place including even its nose.
"Previously, only skulls and bones were found. This find is of great importance for the whole world.'
The remains were found by reindeer herders on the island and the remains will be analysed by scientists at the North-Eastern Federal University (NEFU) in Yakutsk, which is at the forefront of research into extinct woolly mammoths and rhinos.
Russian and foreign colleagues will be invited to join the study.