The 23-year partnership is due to begin in March 2011 and covers everything from collecting and recycling household waste to street cleaning, property design and maintenance.
All 600 council services staff will transfer to Enterprise, with their terms of employment protected under TUPE regulations.
Councillors hope the strategic partnership will improve public services and deliver the best value for taxpayers.
Enterprise has grown rapidly over the years from a simple utility contractor to a major outsourcing company employing 13,000 people across 150 locations in the UK.
Councillor Matthew Lee said, “Looking ahead, the partnership gives us the opportunity to improve the range and quality of services we provide and use Enterprise’s experience, systems and economies of scale to do it more efficiently.”