BCCI President N Srinivasan congratulated the team, which was led superbly by unbeaten centurion skipper Unmukt Chand in the final against the defending champions.
Chand led from the front with a magnificent 111 as the Indian colts beat Australia by six wickets.
"Many congratulations to the Indian team for winning the ICC Under-19 Cricket World Cup. We won the `senior` World Cup last year, and now our boys have triumphed in the junior version of the tournament.
This is a great day for Indian cricket. The Board would like to announce a cash prize of Rs 20 lakh to each player, and Rs 15 lakh to each member of the support staff," Srinivasan said in a statement.
This was India U-19s first triumph after Mohammed Kaif and Virat Kohli led their respective teams to victory in 2000 and 2008 editions respectively.
BCCI secretary Sanjay Jagdale also extended his wishes to the Indian team and said every member of the squad worked hard towards this victory.
"The Indian cricket team has played some extraordinary cricket in the ICC Under-19 Cricket World Cup. The members of the team have worked hard, and deserve the title. Heartiest congratulations to the boys and support staff for winning the World Cup," he said.