Miller Smith, a former chair of Scottish Power, is a senior advisor at Warburg Pincus and also works as an advisor to Goldman Sachs and HSBC. He also serves on the board of builder Firstsource, another business backed by Warburg Pincus.
He worked for Unilever for 30 years, ending his time there as director of finance, and served as chief executive then chairman of ICI between 1995 and 2001.
Miller Smith's appointment fulfils one of the conditions set down when Warburg Pincus bought a 15.7% stake in Premier for £99m in March. The investment group acquired its stake when Premier issued a raft of new shares to pay down some of its £1.8bn debt.
Warburg Pincus gained the right to appoint a non-executive to the board but is barred from increasing its stake within the next 18 months. After that period, it has agreed not to make a bid for Premier until at least six months after its representative quits the Premier board.
"We are delighted to welcome Charles to the board," said Premier chairman David Kappler. "He brings a wealth of experience in both the consumer goods and financial markets, which will enable him to make a valuable contribution to the board and support the achievement of the company's strategic goals."
Shares in Premier are trading at 43p, up more than 50% since Warburg Pincus took its stake three months ago.