Rane quit the Congress and joined the ruling BJP last week. BJP MLA Godinho, who represents Dabolim assembly constituency, joined the saffron party in December last year, months before the assembly polls.
They were administered the oath of office and secrecy by Governor Mridula Sinha at Raj Bhavan.
On March 14, Parrikar inducted nine ministers.
With the induction of Rane and Godinho, the total number of ministers (including Parrikar himself) has gone up to twelve-- five from the BJP, three from Goa Forward Party, two from the MGP and two independents.
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Rane, who was elected on a Congress ticket from Valpoi, quit the Congress and resigned his assembly membership after the party failed to form the government in Goa despite emerging as the single largest bloc winning 17 seats in the 40-member Assembly.
Rane, son of Congress veteran Pratapsinh Rane, who himself won his 11th term as a legislator in the last polls, defied the Congress whip to vote against the trust motion brought by Parrikar by absenting himself from the House.
He joined BJP last week in the presence of Parrikar and other leaders.
Godinho, who has been representing Dabolim assembly constituency since 1994 (till date), was a minister in the Pratapsinh Rane-led cabinet. He was also was the Deputy Speaker of Goa assembly during the Digambar Kamat-led government.