Designed to help improve the effectiveness and efficiency of the professional body for solicitors in England and Wales, the deal covers the society's server and network infrastructure and key business systems.
The organisation is making changes to its operation in readiness for a new framework for regulating the legal profession, expected in the forthcoming Regulation of Legal Services Bill.
The society is also redesigning its membership services. It said LogicaCMG would support these changes.
Judith Hetherington Smith, director of ICT at the Law Society , said, "The partnership with LogicaCMG will deliver savings and enhanced efficiency."
As part of the deal, infrastructure will be transferred to LogicaCMG's Bridgend facility, and support for legacy applications will be provided mainly from LogicaCMG's Birmingham site.