Under the agreements, HP will manage BT's midrange and desktop IT infrastructure in the UK, and BT will manage HP's voice and data network and product support call centres in Europe, the Middle East and Africa.
The move is the first step in a global partnership signed last week that will allow the two organisations to offer joint services to European businesses and the UK consumer and small and medium-sized business markets.
BT and HP said they were evaluating the development of propositions in segments, such as IT infrastructure, application management, workplace solutions and contact centre services.
Ben Verwaayen, chief executive at BT, said, "In a consolidating industry, we believe it makes sense to create a strong alliance between a world-class communications company and a global IT company."
BT has secured more than £2m of business from the NHS national programme for IT, including a contract to build the electronic care records system at the heart of the national programme. BT will also supply the NHS with a broadband infrastructure and it has been awarded a £996m, 10-year contract to be local service provider for London.
The contracts are the biggest in BT's history, and chairman Christopher Bland said the company was excited by the challenge but "somewhat frightened by the enormity and complexity of it".