Sir Roger, who stepped down as president of the CBI lobby group earlier this week, will replace Dick Olver, who has held the role for nine years.
Sir Roger, 66, was chairman of Cadbury during its £10 billion takeover by Kraft and has been chairman of British Gas owner Centrica since 2004.
He will join the BAE board as chairman designate in October and will succeed Mr Olver in the first quarter of 2014. He will quit the role at Centrica next year.
The appointment required clearance from the Ministry of Defence, which has the power to veto an appointment through the Government's special share in the company.
The BAE post is one of the highest profile in the City as the company employs about 100,000 people worldwide and is a major player in the US defence market.
It builds the Typhoon fighter jet and nuclear submarines and provides companies and governments with cyber security. Last year, BAE failed in an attempt to merge with Europe's EADS, the owner of Airbus.
BAE's senior independent director Nick Rose said Sir Roger was the "outstanding" candidate with two decades of board-level experience. He added: "His skills, reputation and relationships with investors and government ministers will be of considerable value to the company both at home and abroad."
Sir Roger said he felt privileged to be offered the role: "BAE Systems is strategically important not just for the UK but internationally, playing a key role in the defence industry in the US and in other parts of the world."