The border guards arrested the pair for failing to have proper immigration papers in Jammu.
During an interrogation, the boys, from a village outside Kabul, said they walked for 18 days through Jallalabad in Afghanistan and the Pakistani cities of Peshawar, Rawalpindi and Sialkot to reach India and try to meet actor Bachchan.
Kasim Din, 17, and his 14-year-old friend known only as Hikmat also wished to meet Bollywood star Shah Rukh Khan and former film great Dharamendra, the report said.
"Afghanistan is fascinated with Bollywood films and (actor) Sholay is the all-time favourite of the people there," one of the boys told interrogators, the report said.
The two were currently in Arnia police station in Jammu.
A spokesman for India's border guards, Prem Singh, told that although the two boys were minors, they would still "have to face the law.