Mr Peston's move follows the departure of Jeff Randall who has since joined the Daily Telegraph as Editor at Large.
He previously worked at The Sunday Telegraph as city editor and at the Financial Times as political editor.
His new role will involve working across a range of news outlets, including Radio Four's Today programme and the Ten O'Clock News.
Commenting on his new role, Mr Peston said: "Jeff Randall transformed BBC business journalism. If it's not tempting fate, my job is to build on that achievement."
Fran Unsworth, head of newsgathering at the BBC, added: "Robert makes for a great successor to Jeff Randall. He brings enormous expertise to the role and has the ability to relay the significance and relevance of business developments to all audiences."
Mr Peston will start his new role in the New Year.
More news from journalism.co.uk:
Murdoch tops Guardian media power list
Profile: Pete Clifton, head of BBC News Interactive
Head of BBC News Interactive announced
Free daily newsletter
If you like our news and feature articles, you can sign up to receive our free daily (Mon-Fri) email newsletter (mobile friendly).
Related articles
- The Telegraph rolls out new 'authored analysis' strategy for editorial newsletters
- Press+ riding the wave of the metered model into Europe
- BBC tells Parliament use of private eyes 'not ruled out'
- Mail bid to block anonymous Leveson witnesses refused
- Telegraph paid middleman £150,000 for expenses data
