Dravid was first appointed as the coach for the two teams in 2015 and under his leadership the youngsters have achieved outstanding results, at home and away.
In his first assignment as coach, the 'A' side won the triangular series in Australia which also had South Africa as the third team.
He repeated that success with the Under-19 team as well, guiding them to the final of the World Cup in 2016.
"Over the last two years, Rahul Dravid has been instrumental in getting young talent into the mix who have proved their worth on the big stage," the BCCI Acting President, CK Khanna said.
BCCI acting secretary, Amitabh Choudhary said that Dravid was instrumental in grooming the youngsters in the last two years.
"Rahul Dravid is known for the discipline and commitment he brings to the table. He has been successful in grooming the youngsters in the last two years. I wish him all the very best for his assignments with the two teams for the next two years," Choudhary said.