Kiszely, in a letter to the Legion's national chairman John Farmer, said it was "inappropriate... To remain as National President of the Legion".
He was one of several retired officers secretly filmed by the Sunday Times, allegedly saying he could influence decision-making over arms deals. Kiszely, however, denies breaking any lobbying rules.
In the footage, seen by BBC News, Kiszely is shown saying he would be able to speak to the prime minister, the defence secretary and the chief of the defence staff at a Remembrance Day event.
"You are standing there waiting for the Queen with nothing else to talk about," Kiszely said.
In his letter of resignation, Kiszely said he had always kept his "role of national president completely separate from any business interests".
Kiszely added he had "never used any access gained as president to raise the subject of, or discuss, any business interests whatsoever, let alone to make representations on behalf of clients.
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"But I made exaggerated and foolish claims to the contrary, incompatible with my position in the Legion."
Kiszely said he was due to step down in December 2012, but believes it is "in the Legion's best interests" for him to stand down immediately.
The Royal British Legion is the UK's leading Service charity. It provides practical care, advice and support to serving members of the Armed Forces, veterans of all ages and their families.