Ford was offered the job on Saturday after a meeting with the India board.
"I am honoured that India have shown such interest in my capabilities, but feel this is the right decision for me and my family," said the South African.
Middlesex supremo John Emburey was also interviewed in Chennai and said: "I'm not going to make any announcements until I've spoken to the India board."
Given that only two candidates were in the frame for the job, Emburey may yet have the opportunity to orchestrate India's star-studded line-up.
The 54-year-old former England off-spinner revealed: "The BBCI haven't spoken to me yet but I understand they've been trying.
But India officials are due to meet on Tuesday and it is possible that new candidates could now be considered. Ford, 46, spent two years as South Africa coach until 2001 and joined Kent in January 2005.
His contract with the English county team expires in 2008 but he was given permission to travel to India and discuss the coaching role of their national team, one of the most high profile positions in sport.
"It has been a really difficult decision," he said.
"I have had a chance to reflect on the offer made by the BCCI and their urgency to fill the vacant position. After careful consideration, I have decided to continue my work here at Kent."
Kent chairman Graham Johnson said: "I know that all in the business at Kent, the playing staff, the coaching staff and all our administrators will be thrilled by his decision." Ford was chosen by a seven-member panel, headed by India board president Sharad Pawar and which included former captains Sunil Gavaskar, Srinivas Venkataraghavan and Ravi Shastri.
Former Indian captain Ajit Wadekar criticised the board for announcing Ford's name before he had accepted their offer.
"The board jumped the gun. Now they are left with nothing," he said.
BCCI treasurer N. Srinivasan told a news conference in Bangalore that Ford had sent a letter to explain his decision.
"He was selected and...it was only a matter of informing us as to when he would be able to join. Therefore, the board announced it had selected him," Srinivasan said.
"He had said that he would let us know when he could join but he has said he can't join us now. That is all."
India are looking for a successor to former Australia captain Chappell, who quit after India crashed out in the first round of the World Cup in the Caribbean.