"The consistency and steadfastness with which you have reposed trust in me, a non-political participant in our public life, has touched me," he said in a letter to her.
Conveying sincere thanks to Banerjee for having thought of him and suggesting his name to UPA partners as a candidate for the post of vice-president, Gandhi said he would always cherish the love of the people of West Bengal, where he served as governor from 2004 to 2009.
"I see it as a reflection of the overwhelming affection which the people of West Bengal have extended to me, something which I shall always cherish and can never forget," he said.
The Congress-led alliance has announced Vice-President Hamid Ansari as its candidate for a second term, while senior BJP leader Jaswant Singh is NDA's nominee.
Trinamool Congress had proposed the names of Gandhi and Krishna Bose, a former Parliamentarian and wife of Netaji Subash Chandra Bose's nephew Sishir Bose, for the post.