The Prime Minister's Office tweeted photographs of the two leaders shaking hands and then sitting for discussions.
Corbyn, the 66-year-old socialist who was elected the leader of Labour Party in a landslide victory two months ago, is among 46 British MPs who have signed a parliamentary motion asking Prime Minister David Cameron to raise human rights issues with his Indian counterpart Modi.
The outspoken extreme left-wing MP was not in the royal gallery when Modi addressed the parliamentarians on Thursday.