O'Driscoll - so often Ireland's lead attacking threat throughout the seven-week tournament - received 2,466 votes through the BBC Sport website poll.
Williams - the scorer of three tries in the 2005 campaign, with a memorable second-half brace against France - gained 7,796 votes with Wales winger Shane Williams coming in third on 2,066.
The 29-year-old Williams said: ''It's a great honour to be named RBS Player of the Championship especially as this is voted for by rugby fans.
Leinster and Ireland centre Gordon D'Arcy took the coveted award last year - polling half of the 12,000 votes collated with international team mate Paul O'Connell second.
Due to a groin injury, the 25-year-old D'Arcy played just 29 minutes of this year's Championship, in the 28-17 opening weekend win over Italy.