Alliance & Leicester said the move would bring significant savings by cutting administration costs and allowing it to consolidate training providers.
Under the deal, QA will take over training administration and course booking and will manage third-party training companies if QA is unable to supply training itself.
Carole Ratcliffe, head of planning and control at Alliance & Leicester, said the three-year contract would give the company access to high-quality training courses that are tailored to match the firm's business strategies and priorities.
QA plans to offer full-day training courses, coaching and customised workshops to Alliance & Leicester staff, in subjects ranging from systems support to software development and end-user skills.
As part of the contract, one member of Alliance & Leicester's training staff will transfer to QA to manage course enquiries and book training.