The animals began to appear in the islands about five years ago after possibly being deliberately introduced.
The report commissioned by Scottish Natural Heritage (SNH) has warned they could significantly impact populations such as voles and hen harriers.
It is feared this, in turn, could affect tourism.
Graham Neville of SNH said: "Orkney is fortunate to have such a diverse and high quality landscape and natural heritage - rich in bird life from Arctic tern, with one of the longest of all migratory passages, to short eared owl and red throated diver.
"Arable land complements cliff colonies and the seas around Orkney are teeming with life and marine plants.
"That makes it plain we have a duty to conserve its nature. And the report tells us it is highly likely that invasive non-native stoats will change the ecology of Orkney. That will have a heavy impact on its place as a home for birds of prey and other species.
"This is a significant issue with implications for the affected species of Orkney - but no one should be in any doubt it will be difficult to remove stoats and it will take major funding to achieve removal."
A stoat that found its way to Orkney was released back on the mainland in 2010.
Stoats on Orkney are likely to cause long-term damage to native species and should be managed, a report has recommended.