On Saturday morning, a few thousand people gathered in the viewing gallery set up by the Indian Space Research Agency (Isro) near the launch site to watch the blast off.
It was also broadcast live on national TV where commentators described it as a "magnificent" launch. Isro scientists said the launch had been successful and its "performance is normal".
After an hour and four minutes of flight-time, Isro declared it "mission successful".
"Now it will continue on its journey - it's a very long journey of 135 days, let's wish it [the] best of luck," Isro chief Sreedhara Panicker Somanath said.
Project director Nigar Shaji said once Aditya-L1 reached its destination, it would benefit not only India, but the global scientific community.
Aditya-L1 will now travel several times around the Earth before being launched towards L1.
From this vantage position, it will be able to watch the Sun constantly and carry out scientific studies.
Isro has not said how much the mission would cost, but reports in the Indian press put it at 3.78bn rupees ($46m; £36m).