In the letter, the hugely popular chief minister of Tamil Nadu state says that she has "been reborn" thanks to the prayers of her supporters.
The letter also urged people to vote for her party in upcoming by-elections.
Critics say this could be an attempt to quell fears about the extent of her illness and mobilise her supporters.
The chief minister was last seen in public on 21 September and admitted to hospital a day later.
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Initially, doctors said the 68-year-old was receiving treatment for "fever and dehydration". She was placed under observation and her diet was monitored. But since then there has been a fierce veil of secrecy around her health.
Last Saturday her doctors reportedly said she had "completely recovered" and would go home "whenever she feels fit".
"Due to the continuous prayers by people in Tamil Nadu, in other states and across the world, I have been reborn and I am happy to share this information with you," Ms Jayalalitha said in the letter released late Sunday.
But all her political responsibilities remain with her deputy O Panneerselvam.
A former film star, Ms Jayalalitha has been Tamil Nadu chief minister three times and is virtually revered in the state.
Ailing Indian politician Jayaram Jayalalitha has hinted at a recovery after months in hospital, in a letter released by her party.