RBS bought Citizens for $440m in 1988 and turned it into one of the biggest regional banks in the US.
But now state-owned RBS is cutting operations abroad in order to focus more on its main UK retail business.
It first sold part of the US company in September last year in an initial public offering, then sold another chunk in March this year.
Citizens Financial Group (CFG) said in a statement that completion of the share offer was "expected to result in RBS's complete exit from its ownership stake in CFG's common stock".
RBS was bailed out by the UK government in 2008 and is currently 73% owned by the state.
It has been trying to streamline its business in order to return to profit. It is pulling out of 25 countries, lowering the number that it operates in to 13.
The Royal Bank of Scotland is selling its remaining 20.9% stake in the US bank Citizens.