The club and its Pride Park stadium was acquired from the anonymous receiver of the parent company Derby County Ltd, which went into receivership earlier this week.
Sleightholme becomes chairman, while Jeremy Keith and marketing and communications entrepreneur Steve Harding have joined the new board.
Commented Sleightholme: "It is a great honour to be involved with such a major football club, one that is a well-known institution in British life with an illustrious sporting history.
"It will take time to put Derby back on the right path but that is our aim."
Sleightholme will replace previous chairman Lionel Pickering, who has now severed all links with the club after nine years.
The new board has raised £15million through re-financing although much of that sum is expected to be eaten up by debt repayments.
