Indian Prime Minister Narendra Modi took to Twitter to hail the launch, describing it as a proud moment for the country.
To date, only the United States, Russia, China, Japan and the European Space Agency have successfully launched so-called "heavy" satellites weighing over three tonnes.
The launch, which took place at 5.28 p.m. local time from the Satish Dhawan Space Centre, was the first to use the Geosynchronous Satellite Launch Vehicle Mark-III (GSLV Mk-III) -- known as "fat boy" on account of its size.
Estimated to weigh as much as five fully-loaded Boeing Jumbo jets, or 200 fully grown elephants, the GSLV Mk-III rocket is the largest most powerful launch vehicle India has ever produced, and considered a potential game changer for the country's space program.
"Initially, we launched our satellites from abroad," said D.P. Karnik, the spokesperson for the Indian Space Research Organization. "The Indian space program is now completely indigenous."
Previously, India has relied on paying the French to launch satellites that weighed more than 2,300 kilograms.
The GSLV Mk III can carry up to 4,000 kilograms, almost double the previous capacity available to India's space program.
In a sense, Monday's launch marks a journey of independence that has taken 25 years, said Rajeswari Rajagopalan, head of the Nuclear and Space policy initiative at the Observer Research Foundation.
It is hoped the rocket's payload -- the 3,136 kilogram GSAT-19 communications satellite -- will help bolster the country's internet connectivity and speed. However, the launch represents only the first stage in a longer plan, and it will be some time before people see tangible effects on the ground, said Rajagopalan.
The success of the launch is widely viewed as a major step towards the country's long term goal of becoming a leading player in the multi-billion dollar global satellite launch market.
Cheap labor and government support means that India can launch satellites for a fraction of the price of rival nations.
In 2014, the country launched a Mars probe for less than it cost to make the Hollywood movie Gravity.
While in February this year, its space program broke a world record when it launched 104 satellites at once.