Angels, based in Hendon, North London, is the major costume provider to television and film industries in the UK.
The company has strong historical ties to the BBC and has worked on Extras, Little Britain and Ashes to Ashes.
The BBC costume department comprises over one million costumes. These will be added to Angels' current stock of three million outfits.
The BBC's collection of around 10,000 wigs has been sold separately to a new company formed by former employees of the costume department.
Mike Southgate, chief executive of BBC Resources, said: “We're delighted that the collection will continue to be available to the production community going forward.”
BBC Costume and Wigs ceased trading on Thursday 14 February. Four members of staff will move to Angels.
Last autumn the BBC announced that BBC Costumes and Wigs would be sold off as part of a wider disposal of assets, including BBC Resources.