Bhalan and Ayyanar belong to ruling AINRC while Visweswaran is BJP's Puducherry unit president.
Speaker V.Sabapathy administered the oath of office to each of the three members and they took the oath in Tamil and in the name of God.
With the induction of the three members the strength of Puducherry Assembly has risen to 33.
Chief Minister N.Rangasamy, his ministerial colleagues, Member of Lok Sabha from Puducherry R.Radhakrishnan and AINRC legislators were present.
The Union Home Ministry had communicated to Puducherry government on September 2 its approval of the list of these three members forwarded by the Chief Minister sometime back.
Rangasamy will present the budget on September 11.