Sri Lanka are set to play three Tests, five one-dayers and a Twenty20 international during the tour.
"Dilshan is keen to travel with the team, to try and create a bond as some of the senior players will be joining the squad a bit late," Dilshan's manager Roshan Abeysinghe told AFP.
Sri Lanka Cricket last week allowed its IPL players to stay on in India until May 18, rowing back on a request for them to return by May 5 to prepare for the tour.
Dilshan took over as skipper last week after Kumar Sangakkara quit following Sri Lanka’s defeat to India in the World Cup final in Mumbai earlier this month.
Dilshan has scored 105 runs from five games for Bangalore, who have won two of their six matches in the money-spinning Twenty20 tournament so far.