The FTSE 100 company held pitches for its retained financial comms account earlier this year and is understood to have selected Finsbury after the competitive pitch.
Well-placed sources said Finsbury had beaten Maitland and two other City agencies to secure the business.
3i, which holds stakes in underwear firm Agent Provocateur and restaurant chain Giraffe, had built a long relationship with Maitland.
The agency was appointed to lead 3i's initial public offering in 1994 and took on financial PR work in 2000.
The firm has been through a significant period of change and in May 2010 named Sir Adrian Montague as chairman, replacing Baroness Hogg.
Maitland had also previously held the retained comms account of 3i Infrastructure, the listed buyout firm part-owned by 3i.
However, Maitland lost the brief to Tulchan Communications in early 2010.
3i confirmed the Finsbury appointment but declined to comment further.
The firm has offices in 12 countries across Europe, Asia and North America, and had more than £13bn worth of assets under management, as of 30 September 2010.
3i suffered badly during the recession, losing £1.9bn in 2008, before launching a £732m rights issue in May 2009 to shore up the balance sheet. However, 3i has since returned to profitability.
Its 117 portfolio investments include German-Danish ferry operator Scandlines, coffee and tea chain Cafe & Te, and yacht maker Fairline.
3i grew from the foundations of the Industrial and Commercial Finance Corporation, formed in 1945 by the Bank of England and other UK banks to boost funding for small and medium-sized businesses.