The case drew widespread attention in India, much of it critical of the Norwegian social welfare officials amid a debate about different cultural attitudes to childcare.
The Indian parents, who live in Norway, claimed their children, now aged four and two, had been taken away due to disapproval over feeding them by hand and sharing the same bed -- common practices in India.
The foreign ministry in New Delhi took up the issue with the Norwegian government, but the father of the children later said the children had been removed partly due to his wife suffering serious psychological problems.
The children arrived in New Delhi, greeted by an unruly media scrum and senior government figures.
"We are all here to welcome them," junior foreign minister Preneet Kaur told reporters at the airport.
A court in Norway on Monday had ruled that putting the girl and younger boy in the care of their uncle in India would "make up for the parents' shortcomings in terms of childcare."
Their grandparents received them at the airport and were reported to be taking them to the family home in Kolkata.
"The kids belong to India... I am confident that the uncle will take care of them in the environment of their extended family in India," Foreign Minister S. M. Krishna said in a video statement.
The two children had been cared for by Norwegian social workers since being taken from their parents in May 2011.