75-year-old Dikshit served as Delhi's chief minister from 1998 to 2013, until she lost to Aam Aadmi Party leader Arvind Kejriwal in the December 2013 assembly polls. She was defeated by over 20,000 votes.
The current Kerala governor Nikhil Kumar resigned recently
She represented UP's Kannauj parliamentary constituency between 1984 and 1989.
Earlier in the day, Dikshit had met Union minister Sushilkumar Shinde and the decision to make her Kerala Governor was conveyed to her.
Dikshit currently faces several corruption charges against her including involvement in the 2010 Commonwealth Games.
Days before quitting, Arvind Kejriwal had moved the high court seeking to take back the appeal filed by then Congress government headed by Dikshit.
Kejriwal-led government had said Dikshit will have to defend herself in the corruption case as she is no more the CM and the government lacked the "locus standi" to fight for her.
(With PTI inputs)