Pakistan-born Khawaja, named Australia's test player of the year this week, was the only member of the squad unable to travel and missed a flight on Wednesday because of the visa delay.
A Cricket Australia spokesperson on Thursday confirmed Khawaja's visa had been approved overnight and he was on a morning flight from Melbourne to Bengaluru.
Australia are holding a training camp in Alur, about an hour outside Bengaluru, before the four-test series starts in Nagpur from February 9.
Khawaja on Wednesday posted on social media about being "stranded".
He spent the night at an airport hotel in Melbourne after parting with teammates, local media said.
Khawaja has previously had a visa problem travelling to India when he tried to enter the country in 2011 for the now-defunct T20 Champions League.
