Sir Fred Goodwin, the former chief executive who lured Alemany to RBS, was sacked in March.
Chief executive Sir Fred Goodwin also announced his resignation at the meeting, and was replaced by Stephen Hester.
"Sir Fred Goodwin agreed to stay in post until his successor was appointed and available, " the letter says.
Former chief executive Sir Fred Goodwin was singled out for criticism at the time for his role in RBS's downfall.
Only five board members remain from the bank's former management team under Sir Fred Goodwin, who was ousted in October following the government bail-out.
This is expected to involve a significant retreat from North America, where the bank acquired a big presence when Sir Fred Goodwin was chief executive.
Former RBS chief executive Sir Fred Goodwin told MPs on Tuesday that he "could not be more sorry" for what had happened to the bank.
Later in the session Mr Cameron confirmed that senior civil servants will meet this week to decide whether Sir Fred Goodwin should be stripped of his knighthood.
Before the banking crisis struck, RBS was led by Sir Fred Goodwin, a man who was determined to be in charge of one of the largest banks on the block.
The only perp walk we've seen in Britain has been the giving of evidence to the Treasury select committee (Barclays' Bob Diamond's likely to be taking it the week after next) or the letter from Buckingham Palace to the banker formerly known as Sir Fred Goodwin.
The FSA looked into the question of Sir Fred Goodwin's private life and the possibility that relations in the bank might have been a tad inappropriate - the subject of a super-injunction, partially lifted last May - and concluded the matter was "irrelevant to the story of RBS's failure".
His influential committee was broadcast live across the UK for at least 6 solid hours - his forensic questioning getting under the skin not just of former bank chiefs like Sir Fred "the Shred" Goodwin, but a day later of the men currently in charge of the banks.
The prime minister yesterday said that it was a good thing that the so-called Forfeiture Committee would look at whether Sir Fred should revert to becoming plain Mr Goodwin.
Calls to strip Sir James of his knighthood echo what happened to Fred Goodwin, the former chief executive of Royal Bank of Scotland, who lost his knighthood in 2012 after being held responsible for the biggest annual loss in UK corporate history.
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