A teacher-turned-politician, Patel, 73, will be sworn in as the state's first woman chief minister Thursday.
Addressing BJP legislators, a teary eyed Patel promised to continue the "glorious traditions of her predecessor" Modi, who is set to take over as India's prime minister.
Prime Minister-designate Narendra Modi Wednesday stepped down as the Gujarat chief minister.
Camaraderie among ruling BJP and opposition Congress legislators and leaders in Gujarat marked an emotional farewell to Modi.
In a brief farewell speech at a special session of the state legislature here Wednesday afternoon, Modi thanked the legislators and people of Gujarat for their love, cooperation and support in his stint as chief minister for around 13 years.
"Henceforth, I shall not be able to enter this legislature again - barring some special functions," Modi said in chaste Gujarati as the entire legislature and some 400-plus invited guests thumped desks and loudly cheered him.
"Over my 13 years, in case I have committed any mistakes, or if there were any shortcomings, please forgive me," Modi said in a voice choked with emotion.
"I have the greatest regards for all the people here and I salute them...especially the house chairman and the opposition," he added as his eyes turned moist.
Recalling some past anecdotes with the Congress Leader of Opposition and his old bete-noire Shankarsinh Vaghela, Modi expressed his special gratitude to Vaghela.
In turn, Vaghela got up from his seat and walked up to Modi and felicitated him with a shawl and warmly hugged and congratulated him.
Several legislators from both sides in the house also congratulated Modi on becoming the PM.
In a lighter vein, Modi said that now Gujarati would be spoken in the Prime Minister's Office and it would have a special place for the people of state.
"Even dhokla would be served in the PMO," Modi said amidst laughter, referring to the Gujaratis' favourite lip-smacking snack.
The Gujarat assembly Wednesday held a special session to bid farewell to the outgoing chief minister, who is set to be sworn in as India's next prime minister next Monday.
Later, Modi submitted his resignation to Governor Kamla Beniwal at Raj Bhavan nearby.
Modi led his party to a historic victory in the general election, making the BJP the first non-Congress party to get a comfortable majority on its own in the 545-member Lok Sabha.