CSC, BT and Xansa's Prism Alliance beat IBM and EDS to win the contract at the former Post Office.
The outsourcing is part of a three-year overhaul of Consignia's business aimed at restoring its profitability. Consignia said the deal would generate savings and improve support services.
The consortium will provide Consignia with a full range of IT services including the maintenance of 42,000 desktop computers and the management and development of Consignia's server, mainframe and network infrastructure.
In addition, the consortium will manage some 600 applications and provide a range of professional services supporting business critical systems.
Malcolm Kitchener, Consignia group managing director of business services, said: "CSC, with their Prism Alliance, will help us develop the systems required to achieve our goal of becoming the best postal business in the world.
"The planned outsourcing also provides fresh opportunities for our IT staff to gain experience and build their careers within an organisation where IT is its specialism."
Around 2,000 IT staff are employed by Consignia will transfer to the new operation.
Peter Skyte, leader of the Communications Managers Association section of the Amicus union, which represents most staff, called for urgent talks with Consignia and CSC about the new operation.