Troops captured the island's airport and main city in a dawn raid. It was unknown what had happened to the self-declared president of the island, Col. Mohammed Bacar, the BBC said.
Bacar declared himself president of the Indian Ocean island in elections deemed illegal by the Comoran government and African Union.
Voice of America reported Bacar had gone into hiding when the invasions started Sunday.
Comoran President Ahmed Mohamed Sambi called on Bacar and his backers to "surrender themselves in order to avoid confrontation."
Sambi said the raid would on Anjouan would "free her citizens" and media reports noted the island's residents celebrated in the streets chanting "Bacar is a dog."
Bacar launched a rebellion last year and reports released Tuesday said Comoran troops faced some resistance from his forces near the capital of the island, Mutsamudu, but suffered no casualties.