Many other BJD leaders who have been allotted portfolios in the ministry also took oath along with Patnaik at the swearing-in ceremony held in Raj Bhavan here.
The Congress won eight of Punjab's 13 Lok Sabha seats in recently-concluded Lok Sabha elections. Jakhar, however, lost to newly-minted BJP leader Sunny Deol by a considerable margin of 82,459 votes.
Prime Minister Narendra Modi, who chaired the meeting, will meet President Ram Nath Kovind to handover the resolution that will pave the way for constituting the 17th Lok Sabha.
"Congratulations to @narendramodi and the NDA for their victory in India's election, and to the Indian people for casting their votes in such historic numbers. As the world's largest exercise in democracy, #India's election is an inspiration around the world," tweeted Pompeo.
Prime Minister Narendra Modi and BJP president Amit Shah on Friday visited veteran leaders LK Advani and Murli Manohar Joshi to seek their blessings after the BJP-led NDA won a second term with a resounding majority.
"This is the triumph of the national forces. Many compliments to each and everyone who have contributed to this victory of democracy," RSS general secretary Bhaiyyaji Joshi said.
The BJP on Thursday got an overwhelming majority in the Lok Sabha, crossing on its own the 300 mark while storming back to power for the second consecutive term.
Counting of votes for Lok Sabha and four state assemblies- Andhra Pradesh, Sikkim, Arunachal Pradesh and Odisha- will take place on Thursday.
According to India Today-Axis My India Exit Poll, NDA government is set to come back to power with a landslide majority.The NDA is predicted to win between 339 and 365 seats while UPA is likely to win 77-108 seats.
According to the exit poll survey by Jan Ki Baat, the NDA is set to cross 300 mark, with BJP getting 254-274 seats on its own.