Patel, who has served in former Prime Minister Boris Johnson's Cabinet, switched support after former PM Johnson pulled out of the race on Sunday night.
In a statement on Sunday night, the former Prime Minister said: "In the last few days I have been overwhelmed by the number of people who suggested that I should once again contest the Conservative Party leadership.
Facing Sunak in the second stage - a ballot of the full membership of the Conservative party - will be Foreign Secretary Liz Truss, who obtained 113 votes.
Meanwhile, Johnson has thrown an extraordinary spanner in the works by tabling a confidence motion on his government on Monday.
Bowing to the inevitable after mass resignations across his government, including that of top Cabinet ministers, Johnson on Thursday announced he is stepping down as leader of the Conservative Party, but will remain the UK Prime Minister till his replacement is chosen.
A Conservative leadership race will take place soon and a new Prime Minister will be in place in time for the Conservative Party conference in October, the BBC reported.
For months Prime Minister Johnson has been facing a barrage of criticism and rebellion over his conduct and that of his government, including illegal, Covid-linked lockdown-breaking parties at his Downing Street offices for which he and others were fined by the police.
Johnson has been putting up a strong defence in the face of criticism after voters punished the Conservatives over the partygate scandal and rising cost of living crisis by voting for Opposition Labour and Liberal Democrats in the by-elections earlier this week.
During bilateral talks with his Indian counterpart Narendra Modi, Johnson discussed the ways to boost trade and security ties with India, which buys more than half of its military hardware from Russia.
Prime Minister Modi while addressing the press, said, "He (Johnson) has played a role in strengthening India-UK relations. His coming to India during 'Azadi Ka Amrit Mahotsav' is historic."
Addressing the joint media address after the bilateral talks with British Prime Minister Boris Johnson held at Hyderabad House, Modi said, "Recently we have concluded FTA talks with UAE and Australia. We wish to go for FTA with the UK with the same spirit and commitment.
After his reception, the UK Prime Minister visited Rajghat to lay a wreath on the Samadhi of Mahatma Gandhi.
Indian student numbers have also registered a steady rise since the introduction of post-study work options under the UK's post-Brexit points-based visa system.
During his day-long stay in Gujarat, the British prime minister is scheduled to have a closed-door meeting with prominent business leaders from the state, sources said.
The instigation of London is also unacceptable, which is strongly pushing not only its Western allies, but also other countries to introduce large-scale anti-Russian sanctions, which, however, are senseless and counterproductive, it adds.