Meanwhile, the Indian Navy's stealth frigate INS Satpura and tanker INS Jyoti Mission are also racing against the inclement weather to help in the rescue.
During his solo bid for circumnavigation, Tomy's sailboat "Thuriya" carried specially prepared food items and fresh water in the limited space on board.
On Sunday morning, an aircraft took off to locate Tomy, an Indian Navy officer.
Irishman McGuckin, whose boat also rolled in the storm and sustained minor injuries, has also asked to be evacuated.
"The yacht is severely damaged with gear hanging over the side", added Gaden, an official with the Australian Maritime Safety Authority (AMSA).
Tomy, an Indian naval officer, was in third out of 18 participants before the severe storm hit, and survived on cans of iced tea that were nearby, Sky News reported.
McGuckin's yacht Hanley Energy Endurance, was also dismasted 90 miles to the SW of Thuriya, is the nearest vessel.
Defence minister Nirmala Sitharaman had on Sunday night said that the rescue mission was being coordinated with the Australian Navy.
The French crew plans to take Commander Tomy to a French research facility on Amsterdam Island 100 kilometers (60 miles) to the north.
The race organisers shared messages from him on Twitter where he described his chest burning, vomiting and asking for a "rescue ETA".
A French fisheries patrol boat found 39-year-old after he was able to provide information via text messages, although the battery power of his devices were diminishing.
In its efforts to rescue Indian Navy Commander Abhilash Tomy, who now lies injured in his sailing vessel in the south of Indian Ocean, Defence Minister Nirmala Sitharaman said the officer would be rescued French vessel Osiris in the next 16 hours.
Abhilash Tomy was rescued by a French ship HMAS Ballarat..
The Navy spokesman said Tomy was conscious and was shifted to a French vessel named Osiris.
According to the report, Tomy is responding to radio communications.
Tomy had suffered a serious back injury Friday after his yacht was damaged in a storm while representing India in the global solo circumnavigation Golden Globe Race (GGR) 2018.
Earlier, bad weather was creating impediments in reaching Tomy whose vessel was "rolling excessively" in the South Indian Ocean.