The All Assam Students' Union (AASU), Citizens' Forum, Asom Jatiyatabadi Yuva Chatra Parishad (AJYCP), Krishak Mukti Sangram Samiti (KMSS) and parties such as the Congress and Asom Gana Prishad (AGP) celebrated the development.
AASU adviser Samujjal Bhattacharyya expressed his happiness and complimented the people of the region for standing united against the Bill.
"We condemn the BJP government for failing to ascertain the sentiments of the people of the region," he said.
The students' body also celebrated the victory by signing songs and distributing sweets to its members and passersby in front of the AASU headquarters in the state capital.
However, state Health and Finance Minister Himanta Biswa Sarmathe described the development as a "defeat for Assam."
"It is a defeat for Assam. My party and I extended full support to the Bill. We do not have a majority in the Rajya Sabha, so the Bill could not be passed. Bangladeshi Muslims will now occupy 17 constituencies of lower and central Assam. The people of Assam will lose their culture and language," Sarma said.
The KMSS and AJYCP also celebrated the development and said the people of the region have given a strong message to the ruling BJP governments in Delhi and Assam, saying the party will face the consequences in the forthcoming general elections.
The Congress in Assam also rejoiced at the Modi government's failure to push through the contentious Bill in the Rajya Sabha and said the party has yet again foiled an attempt by the communal forces to convert secular India into a fundamentalist nation.
Debabrata Saikia, the leader of the Opposition in the Assembly, said the Congress honoured the sentiments of the people of Assam and the North-East.
Lauding the effective floor coordination between the Congress and non-BJP parties, Saikia said the Modi government was unable to muster the courage to table the Bill in the Rajya Sabha on the last day of the Budget session.