"There will be a day when we will all be free in places that no-one knows," he said in a video posted on Twitter.
"My destiny brought me here to Geneva, Switzerland but your destiny will take you somewhere else. It could take you to New Zealand or to Australia or to the United States."
He said his "good news" was overshadowed by sadness over the continued detention of refugees and asylum seekers under Australia's offshore detention policy.
"For the first time in 6 years am free, but I won’t be truly free in my heart till everyone of my brother and sisters on Manus/Nauru are free and well in safe country," he said.
In February, the Sudanese refugee accepted a major human rights award in Geneva, Switzerland.
Refugee flown from Manus Island to Switzerland to accept major human rights award
Officials in Switzerland granted Mr Muhamat a temporary visa at the time, which allowed him to travel to Geneva for the awards ceremony.
Mr Muhamat said he will continue to speak out against Australia's offshore processing policy and support other detainees on Manus Island.
"Remember this: we fought so hard during our six years together. We are fighting for our dignity and we are fighting for our freedoms. And most importantly we are fighting to change that number into names. We want to use our names -- the names that our parents [gave to us]."
More refugees being treated in Australia than on Nauru and Manus Island
In March, Mr Muhamat spoke before the United Nations Human Rights Council in Geneva urging the body to hold Australia accountable for its policy of offshore detention.
Reflecting on his advocacy on the world stage, Mr Muhamat said he still encountered reactions of disbelief at the extent of the 'cruelty' of Australia's asylum seeker policy.
"The things we have experienced," he said in his video, addressed to those still detained on Manus Island," what we have seen, what we have been through is indescribable.
"And I have found that people are not able to comprehend what we have been through."
Mr Muhamat won the 2019 Martin Ennals Award for his work documenting the impact of his time in Australia's offshore processing detention centre on Manus Island.
He communicated his experiences through social media posts and media interviews.
In 2017, he supplied almost 4,000 voice messages to create the The Messenger podcast, co-produced by the Wheeler Centre and Guardian Australia.
More than 500 refugees and asylum seekers are detained on Manus Island, three years after the Papua New Guinea Supreme Court ruled the detention of Australian asylum seekers on the island was unconstitutional.
The Manus Island processing centre at Papua New Guinea’s Lombrum Naval Base was shut down in November 2017, leaving hundreds of men stranded without valid travel documents.