Dell is the world's largest personal computer manufacturer and spends more than £12 million on UK advertising across eight brand divisions.
It is understood the work BMP will handle will include TV and press.
Dell has never had a pan-European agency.
The bulk of Dell's creative work is handled by cdp-travissully and WWAV Rapp Collins Scotland. Media planning and buying across all of Dell's product divisions is handled by Carat.
Dell competes with heavyweights such as IBM, Hewlett-Packard and Sun Microsystems and has about 20 per cent of the global market. In Europe, Dell products account for about 12 per cent of all personal computers sold.
As well as selling to consumers, Dell provides infrastructure and services for client companies including American Airlines, the recruitment website Monster. com, the car manufacturer Toyota, the pharmaceutical giant Bayer and the telecoms company AT&T.
The company has annual sales of more than $32 billion.
No-one from Dell or BMP was available to comment as Campaign went to press.