Both Heaslip and O'Driscoll have been in magnificent form for Leinster, Ireland and the British & Irish Lions in 2009.
But the star pair were pipped to the Game's most prestigious individual award by New Zealand openside Riche McCaw.
The All Black skipper became the first player to claim the award on two occasions as following his first success three years ago.
McCaw takes over from Ospreys and Wales wing Shane Williams who picked up the accolade in 2008.
"It is a huge honour. I am extremely proud," said McCaw, who was chosen ahead of Springboks Fourie du Preez and Francois Steyn, England's Tom Croft and Ireland's Heaslip and O'Driscoll.
"I am just happy to be part of a team doing well. I am happy to do my bit, but it is a great honour.
"I said it before, you can't do it without a bunch of mates. It has been a trying year at times, but it is great to be part of a winning team."
O'Driscoll had been the bookmakers' favourite to join 2001 winner Keith Wood as the second Irishman to receive the honour but the Leinster talisman was surprisingly overlooked by judges John Eales, Will Greenwood, Gavin Hastings, Raphaël Ibanez, Francois Pienaar, Agustin Pichot, Scott Quinnell, Tana Umaga and Paul Wallace.
There was at least cause for celebration for Ireland coach Declan Kidney, however, as he was crowned IRB Coach of the Year having led his country to a first Grand Slam since 1948.
Kidney had seen his side end 2009 with a 15-10 defeat of Tri Nations Champions South Africa earlier on Saturday night but, despite that result, the Springboks still claimed the IRB Team of the Year award.
IRB World Player of the Year winners list
2001 - Keith Wood (Ireland)
2002 - Fabien Galthié (France)
2003 - Jonny Wilkinson (England)
2004 - Schalk Burger (South Africa)
2005 - Daniel Carter (New Zealand)
2006 - Richie McCaw (New Zealand)
2007 - Bryan Habana (South Africa)
2008 - Shane Williams (Wales)
2009 - Richie McCaw (New Zealand)
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