The US-based investment bank is to take on Quilter from its rival, Morgan Stanley, with the intention of merging the UK firm into its wealth advisers division.
Terms of the deal have not yet been released by either group, although the firms revealed that Quilter currently handles assets in the region of $11 billion and has 18,000 clients, served by 3,000 staff.
Quilter's chief executive, Martin Baines, has been confirmed as remaining in his current role as chief executive of the company and he will report to Marianne Hay, head of Citigroup's European wealth management operations, as well as to John Longley, head of Citigroup Wealth Advisors.
Todd Thomson, chairman and chief executive of Citigroup Global Wealth Management, described the acquisition as "an important step" as the company looks to build "a meaningful presence in the UK".
Mr Thomson added the deal gives Citigroup "an excellent platform to support the further growth of our Private Bank and international Smith Barney businesses".