"Congratulations to Jayalalithaa ji and her team on taking oath. Centre will work closely with new government for progress of Tamil Nadu," Modi said in a tweet.
Jayalalithaa, 68, who controls AIADMK as its general secretary, on Monday took oath in Chennai as Tamil Nadu's chief minister. Twenty eight ministers were also sworn in.
The AIADMK-led front won 134 seats in the recently concluded elections for the 234-member assembly.
Her party has twice been a member of the BJP-led National Democratic Alliance (NDA) but is currently out of the coalition.
Notwithstanding political differences, Jayalalithaa and Modi have been maintaining good relations. Modi had attended Jayalalithaa's swearing-in as Gujarat chief minister in 2011.
On December 26, 2012 when Modi was sworn in as the chief minister of Gujarat for the fourth consecutive term, the presence of Chief Minister Jayalalithaa had added its own flavour to the entire show.