The team profiles on the official BBC Sport website were updated on Wednesday night (January 11) to include Anderson, along with the corporation's former Moto GP anchor Jennie Gow.
Anderson started his F1 career in the 1970s. He has served as technical director at Jordan Grand Prix - now Sahara Force India - and the Stewart and Jaguar racing teams.
He also contributes to motorsport publications including Autosport and has worked on F1 coverage for Irish broadcaster RTE and the ESPN Star Sports network in Asia.
Gow filled in as BBC Radio 5 Live's pitlane reporter at last season's Canadian and Hungarian grands prix. She replaces Natalie Pinkham, who has moved to Sky Sports F1 along with David Croft, Ted Kravitz and Martin Brundle.
Ben Edwards replaces Brundle as the BBC's lead television commentator, while former ITV commentator James Allen confirmed last week that he is joining BBC Radio 5 Live as its lead commentator and F1 correspondent.
The BBC's head of F1 Ben Gallop hailed the new recruits' "wealth of experience and knowledge" and their "huge passion for the sport" in a statement issued on Thursday morning (January 12).
Jake Humphrey, David Coulthard and Lee McKenzie will stay with the BBC's F1 team, while Eddie Jordan is also staying with the corporation.
> ITV drops Formula One website after 12 years
> BBC's Mark Thompson defends controversial Formula One deal