An LBG spokeswoman said Gilbert had taken the decision for 'personal reasons', and was 'keen to explore other opportunities' in marketing.
She also confirmed that the bank has launched a search for a replacement both within the company and externally.
In the interim, its marketing will be handled by Catherine Kehoe, head of brand and customer marketing for Lloyds TSB, Steven Griffiths, head of brand and customer marketing for Halifax and Bank of Scotland, and Joe Clift, LBG's group brand and customer marketing director.
Gilbert, previously marketing director at Lloyds TSB, was appointed to the top marketing job at LBG in December 2008.
The former chairman of Lowe Asia Pacific was chosen ahead of Philip Hanson, his equivalent at HBOS, for the overarching position.
During his time in charge, Gilbert has been responsible for the development of Lloyds TSB's sponsorship of the London 2012 Olympics, and its long-term marketing strategy, based on the strapline 'For the journey'.
Last month, Gilbert oversaw the hiring of Mediaedge:cia to LBG's £80m media planning and buying account, following a four-way pitch.
LBG has come under pressure from the EU competition authorities to sell off some of its businesses. It is reviewing a decision to close its Cheltenham & Gloucester subsidiary.
Nigel Gilbert CV
- 1998-2006: Worldwide account director, rising to chairman and chief executive, Lowe Asia Pacific
- 2006-2008: Group marketing director, Lloyds TSB
- 2008-09: Group marketing director, Lloyds Banking Group