Eman Ahmed Abd El Aty, 36, will be flown on a chartered plane to Mumbai where bariatric surgeon Dr Muffazal Lakdawala plans to operate.
The Indian embassy in Cairo initially denied her visa request as she was unable to travel there in person.
After the surgeon tweeted to India's foreign minister that changed.
India's External Affairs Minister Sushma Swaraj, who is herself in hospital awaiting a kidney transplant, was quick to respond with an offer of help.
Ms Abd El Aty's family says she hasn't been able to leave home for 25 years now and claims she weighs 500kg.
If the claim about her weight is true, then that would make her the world's heaviest woman alive as the current Guinness record holder is Pauline Potter of the United States who weighed 292kg (643lb) in 2010.
Dr Lakdawala, who has performed weight reduction surgeries on Indian minister Nitin Gadkari and Venkaiah Naidu, told the BBC that from looking at Ms Abd El Aty's medical reports and photographs, he believes that she weighs at least 450kg.
Ms Abd El Aty's family says she weighed 5kg (11lb) at birth and was diagnosed with elephantiasis, a condition in which a limb or other body parts swell due to a parasitic infection, Dr Lakdawala told the BBC in a phone call from Mumbai.
"They said when she was 11, she had gained immense weight because of which she could not stand up and would crawl.
"And then she suffered a stroke which left her bedridden and she has not been able to leave home since then."
Ms Abd El Aty is cared for by her mother and sister.
Dr Lakdawala said Ms Abd El Aty's sister got in touch with him in October and he began raising money to bring her over to Mumbai as her family was too poor and unable to bear the costs of chartering a flight.
"We are expecting to fly her to Mumbai next week as soon as the formalities are over," he said.
Dr Lakdawala believes that Ms Abd El Aty does not have elephantiasis, but suffers from obesity-related lymphoedema which causes gigantic swelling of legs.
"She would need to remain in Mumbai for two to three months for the surgery and treatment after which she would be able to return home, but it would take two to three years to bring her body weight under 100kg," the surgeon said.
"I'm hopeful that I will be able to help her, I won't say I'm confident because I think that would be an exaggeration," he added.
Bariatric surgery, also known as weight loss surgery, is used as a last resort to treat people who are dangerously obese and carrying an excessive amount of body fat.
In the UK, this type of surgery is available on the NHS only to treat people with potentially life-threatening obesity when other treatments have not worked.
Around 8,000 people a year in the UK currently receive the treatment.
The two most common types of weight loss surgery are:
Where are you on the global fat scale?

The service said it had a shortage of 24 staff - the equivalent of 12 ambulance crews - that could have led to delays for "less serious calls".
It said support was sought from voluntary and private ambulance crews.
The shortage was due to a factors including rostered leave, sickness, vacant shifts and cancelled overtime.
John McPoland from the NIAS said the shortage left the service about 20% down on the usual 60 crews it expected to have in place for a Saturday night shift.
He added that the staff shortage was an ongoing issue.
"We are experiencing difficulty at the weekend and we have been relying on the voluntary crews and on the private ambulances," he said.
"We also rely on our staff coming in and doing overtime.
"We have been dealing with situations like this for quite a while now.
"We're absolutely not happy about it but we will take steps to try to address it."
He added that the reduced service would mostly be felt by patients "whose situation is not immediately or potentially life-threatening".
An Egyptian woman, believed to be the world's heaviest woman at 500kg (1,102lb), will soon be flown to India for weight reduction surgery.
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The Northern Ireland Ambulance Service (NIAS) has said it had to operate a reduced level of cover on Saturday night due to a shortage of staff.