A Rashtrapati Bhavan communique said that President Pranab Mukherjee had accepted the resignation of Dikshit, a former chief minister of Delhi and a senior Congress leader.
The communique said Sathasivam would be the governor "with effect from the date he assumes charge of his office".
According to TV reports, Sathasivam told media-persons, "I haven't accepted any corporate arbitration. Will serve the people of Kerala."
"I won't give legal opinion as Governor", he further said.
Justice Sathasivam retired as the CJI in April this year.
Meanwhile, earlier in the day, the Congress was caught in a rift as two leaders voiced contradicting opinion on the appointment of former chief justice of India P. Sathasivam as the Kerala governor.
While Congress spokesperson Anand Sharma slammed the government for patronising retired judges, Manish Tewari said no motive can be attributed to Sathasivam being appointed governor of a state.
Later, the All India Women's Congress president Shobha Oza downplayed Tewari's comments saying it was his personal opinion.
"We have made it crystal clear that whatever party spokesperson Anand Sharma has said on the issue is the official party line and any other person speaking on the issue is their personal view," Oza told the media.
Tewari had told a TV news channel that there was "no constitutional or legal bar on a former CJI to becoming a governor".
This was in sharp contrast to Sharma's statement on Tuesday.
"(Former) CJI of India should not be open to government patronage. This is sending wrong messages and raising doubt," Sharma had said.
(With agency inputs)