Parrikar quit as the defence minister of India, a post he had been holding since November 2014 after first reshuffle of Prime Minister Narendra Modi's Cabinet.
Parrikar replaced incumbent Chief Minister Laxmikant Parsekar.
Parrikar has been Goa's Chief Minister twice before and has been credited with strengthening the BJP in the coastal state.
The BJP, which won 13 seats in the 40-member Goa Assembly, managed to garner support from other parties and Independents to attain majority under Parrikar.
Three MLAs of the Goa Forward Party, three of the Maharashtrawadi Gomantak Party (MGP) and two Independents have pledged their support to Parrikar.
The Congress won 17 seats in the recently concluded polls.
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