The Bhagirathi is traditionally regarded as the source stream of the Ganges River.
It rises at Gaumukh, the snout of the Gangotri Glacier in Uttarakhand, India. The river flows through the Garhwal Himalayas before meeting the Alaknanda at Devprayag. At that confluence, the combined river officially takes the name Ganges, or Ganga.
The answer can seem confusing because the Alaknanda carries greater discharge at Devprayag and is sometimes described by hydrologists as the main headstream. In Hindu tradition, however, the Bhagirathi has special importance because King Bhagiratha is believed to have brought the heavenly Ganga to Earth.
The Bhagirathi is not the same river as the Brahmaputra, Indus, or Yamuna. Those rivers also rise in or near the Himalayas, but they follow different drainage systems across South Asia.