His appointment comes at an important time for the struggling media company, which has recently been the subject of speculation about a merger with Fairfax Media - in which Rinehart holds a 15 per cent stake.
But analysts still believe a merger has major hurdles to clear - including asset sales to meet media ownership laws.
Ten's managing director Hamish McLennan thanked Rinehart for her contributions to the company in her three years on the board. "It has been a very great pleasure working with Mrs Rinehart," he said.
Rinehart, Australia's richest person, is expected to hold on to her 9.7 per cent stake in Ten. "I look forward to her ongoing involvement," McLennan said.
He also welcomed Mr Klepec to the board, highlighting his experience in business development at Hancock and other companies, including BHP Billiton.
Shares in Ten were higher in morning trade, but finished Monday steady at 22 cents.
- AAP