MCBD won the account after a three-way pitch against Leagas Delaney and another unnamed agency.
Boxclever is the result of the £1 billion merger of Radio Rentals and Granada in December 1999. Since then, the company has been streamlining its business but is now looking to revitalise the declining TV rental market.
MCBD will assist in developing Boxclever's business proposition while refocusing the brand and attempting to give it a more modern appeal to today's consumers.
The account is believed to be worth £1 million at present but could rise to an estimated £8 million next year.
David Cowan, Boxclever's chief executive, said: "MCBD really impressed us with its thinking and approach and we're delighted to be working with it."
The campaign, which will break later this year, is expected to play on consumers' fears that technology is constantly evolving and that rental is the most sensible option to avoid being left with outdated equipment.
Helen Calcraft, the MCBD managing director, said: "This is the sort of assignment we relish at MCBD as it allows us to get close to the development of a business and take a holistic view of the role the communications disciplines can play in its success."
The Boxclever account was previously handled by Granada's agency, Abbott Mead Vickers BBDO, which won the business after seeing off competition from the Radio Rentals incumbent agency, Ogilvy & Mather.
However, Boxclever split from AMV back in July 2001 after a two-year partnership and has produced little in the way of advertising since.