"He is getting a good position, he has achieved this. I am very happy," Balakrishnan's octogenarian mother KM Sharda told India's NDTV television network after attending the event.
The new chief justice was born in a village in the southern state of Kerala, and comes from a poor background.
A handful of Dalits, the name adopted by the group, have made it to the country's top posts in recent years, including the former president KR Narayanan, who died in 2005.
The caste system in India is still enforced in rural parts of the country where Dalits are sometimes expected to carry out the most menial tasks and have been forbidden from using the same drinking water as higher castes.
Many have converted to Buddhism in an attempt to escape prejudice.
Indian society has tried to get around this divisive culture by maintaining quota systems, ensuring that some from the lowest castes do reach positions of authority.
But these do not extend to rural communities. Dalits, make up about 16 per cent of India's 1.1 billion population.
Nearly 60 per cent of Dalits live in the Uttar Pradesh, West Bengal, Bihar, Andhra Pradesh, and Tamil Nadu states.
Balakrishnan said when his appointment was announced last year that his initial focus would be on ensuring that honest people enter the judiciary.
"We have to carefully scrutinise the antecedents of judicial officers and block the way [of corrupt people] right at the entry level," he was quoted as saying in The Times of India.