The sailor, Indian naval commander Abhilash Tomy, called for emergency aid on Saturday after the yacht was badly damaged in a storm about 3,500 km (2,175 miles) west of the Australian coast, leaving him with severe back injuries.
Tomy, 39, was sailing solo as part of the Golden Globe Race (GGR), which involves travelling 30,000 miles (over 48,000 km) to circumnavigate the globe.
A seriously injured Indian sailor is likely to be rescued in the next few hours, as a French fishing vessel nears the location of his yacht.
Race control is relaying messages to JRCC (Joint Rescue Coordination Centre) Australia.
The yacht used by Abhilash Tomy is a replica of the vessel used by famous British sailor Robin Knox Johnston to win the first Golden Globe race in 1969.
The Indian Navy tweeted: "Tomy rescued safely". "Indian Naval stealth Frigate "INS Satpura" operating in the Indian Ocean has been dispatched for the rescue mission", a defence spokesman said in Kochi.
But Indian and Australian officials said a French fisheries patrol vessel involved in the global rescue mission had found the sailor "in a stable condition". Tomy had requested for a stretcher as he was not able to move on his own.
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The Navy's P8I aircraft, which flew from Mauritius early on Sunday, located the "mast broken boat rolling excessively".
His location is said be in the south Indian Ocean, approximately 1,900 nautical miles (nm) from Perth, Australia, and 2700 nm (approx 5,020 kms on ground) from Cape Comorin (Kanyakumari).
Rescuers confirmed "Tomy is conscious, talking and onboard the Orisis", race organisers said in a statement on Monday.
The yachts of Tomy and Ireland's Gregory McGuckin were dismasted by 70-knot winds and 14m-high seas.
His boat, the Thuriya, is a replica of Robin Knox-Johnston's Suhaili, victor of the first Golden Globe Race in 1968.
Race officials had sent messages to Tomy informing him of the latest updates to the rescue plan, but were concerned when he no longer returned their messages, suggesting he was possibly "now too weak to transmit", they said. No modern equipment is allowed except for communication devices.
The Indian-built yacht, Thuriya, left the seaside town of Les Sables-d'Olonne in western France on July 1 in the roundtrip race.