It is the latest in a series of high-profile contracts for the print management firm, which has already won contracts with the BBC and Scottish government this year.
Cheadle, Cheshire-based APS will handle direct and transactional mail for Family Investments, which looks after £2.8bn of investments for 1.7m people in the UK.
Ann McLaughlin, business services director at APS, said: "This deal is a significant move for us in the top of the market. We competed against a number of credible competitors and so this shows we have significant integrity within the market."
McLaughlin added that the £60m-turnover company had had a "pretty good year to date".