Bamford was on the board of Vodafone between 1998 and 2006 and held roles there including chief executive of Vodafone UK from 1999 to 2001 and regional chief executive between 2002 and 2003.
Previously, he has held senior general and commercial management positions at WHSmith, Kingfisher and Tesco.
He is non-executive director of Rentokil Initial and chairman of The Key Revolution.
Woolworths chairman Richard North said: “Peter's extensive retail and general management experience together with his marketing skills further strengthens the board and should provide valuable insight to the management team as we develop our retail and entertainment wholesale businesses.”
Last week, Woolworths announced the appointment of Steve Lewis as EUK managing director to drive sales at its entertainment wholesale arm.
The retailer agreed a four-year refinancing package totalling£385 million with Bank of Ireland and GMAC Commercial Finance.