The two companies will form a joint venture with the council that will be responsible for the strategic management of all property services.
The deal is expected to be worth more than £100m, although there is scope for this to grow by increasing the scale of service delivery, Carillion said.
The council says that it will save 30% of its property budget by 2015/16.
The JV will be called Stockport Strategic Property Partnership (SSPP) and will be established in September 2013. The partnership will initially be for 10 years, with the option to extend this for a further five years.
Staff within the current provider, NPS, will be transferred to the new provider.
Carillion will provide strategic advisory services for estates management, facilities management, energy management and capital projects, with CBRE delivering strategic asset management and development advice. Carillion will also have an exclusive option to deliver operational professional services that are currently delivered by NPS, including estates management and multi-disciplinary design.
SSPP will also have the opportunity to provide similar services to other councils within the Association of Greater Manchester Authorities (AGMA) without the need for further procurement processes or costs.
Services delivered directly to schools and academies in Stockport and other authorities within AGMA will also be part of SSPP's growth plans.
Carillion chief executive Richard Howson said: “I believe this further success in the local authority outsourcing market once again reflects our ability to provide integrated service solutions that enable local authorities to reduce costs without sacrificing service quality."
Deputy council leader Mark Weldon said: "To achieve greater efficiencies and collaboration between public sector agencies to deliver local community services, we are transforming the council's estate and property portfolios. I am confident that the new operating model will deliver an effective and efficient strategic property service to meet the council's future priorities."