Earlier, Anandiben was Wednesday unanimously elected leader of the BJP Legislature Party, paving the way for her to succeed her mentor and become the first woman chief minister of Gujarat.
Modi quit as chief minister Wednesday after leading his party to a stunning victory in the general election. He is to be sworn in as India's next prime minister Monday.
Teacher-turned-politician Patel, 73, promised to carry forward the glorious traditions set by Modi and leave no stone unturned for the development of the state.
Addressing members of the Bharatiya Janata Party (BJP) Legislature Party after her elevation, Patel said she would live up to the expectations of the party and people in her new role as chief minister.
"I shall not betray the trust imposed in me by the party and people of the state, there shall be no let up in the progress of Gujarat," a teary-eyed Patel said in her acceptance speech in chaste Gujarati at the Town Hall here.