Mr Rogers joined Babcock in 2002 and prior to this he was deputy CEO of Acordis.
Current non-executive director Chris Bucknall will retire from the board at the company's Annual General Meeting in November. He held the role from 2000.
Chairman David Calverley said: “I would like to thank Chris for the tremendous contribution he has made to the Company over the years and wish him well for the future.
“We are delighted to welcome Peter, who brings with him significant business experience, which will be a great asset to the board."