The six-man shortlist consists of two nominees from Rugby World Cup 2015 finalists New Zealand and Australia, while Wales and Scotland have one apiece.
Joining Carter and Savea are Australian breakdown masters David Pocock and Michael Hooper, Welsh prop Alun Wyn Jones and Scottish halfback Greig Laidlaw.
World Rugby Chairman Bernard Lapasset said: "Each player thoroughly deserves their nomination and I am sure that the panel will have much to think about over the next couple of days as they determine who will be the recipient of this wonderful accolade."
Daniel Carter (New Zealand)
A two-time recipient of this award, in 2005 and 2012, Carter will play his 112th and final test for the All Blacks in the RWC 2015 final, bringing down the curtain on an illustrious 12-year career in which he has scored a world record 1579 test points.
Desperate to bow out with RWC success, having seen his 2011 tournament cut short by injury, the 33-year-old has been rolling back the years with some impressive performances in recent weeks.
Michael Hooper (Australia)
The youngest of the six nominees, having turned 24 yesterday, Hooper became the fastest and second youngest player to reach 50 test caps in the semi-final win over Argentina. The perfect link man between forwards and backs, he is one third of the formidable Wallabies back row alongside Scott Fardy and fellow nominee David Pocock who have dominated the breakdown at RWC 2015.
Alun Wyn Jones (Wales)
A towering presence in the Welsh second row, Wyn Jones joined the club of rugby test centurions in their quarter-final exit to South Africa, combining his 94 Welsh caps with six for the British and Irish Lions. The 30-year-old anchors the front five and is a fierce competitor, not to mention an inspiring figure on and off the field. He has started all 10 of his tests in 2015, captaining Wales to victory in their warm-up match with Ireland in Dublin.
Greig Laidlaw (Scotland)
Leading by example as Scotland captain, Laidlaw bowed out of Rugby World Cup 2015 in the quarter-finals as the leading point-scorer with 79, 26 of them - including a crucial late try - coming in the 36-33 win over Samoa which confirmed his side's place in the quarter-finals as Pool B runners-up. The proud 30-year-old started 12 of Scotland's 14 tests this year and came off the bench in their pool victory over the USA.
David Pocock (Australia)
The 27-year-old's skills at the breakdown are legendary and he has been a thorn in many a team's side at RWC 2015, unsurprisingly leading the statistics for turnovers with 14 to show he is back to his scavenging best after undergoing two major knee constructions in successive years. Nominated for World Rugby Player of the Year for the third time, Pocock is both a calming and inspirational presence in the Wallabies back row.
Julian Savea (New Zealand)
The All Black winger has a try-scoring rate that few, if any, can match in world rugby, having crossed the try-line 38 times in 40 tests since his debut in June 2012. The 25-year-old, a former Junior Player of the Year who was nominated for this award in 2014, has scored eight tries at RWC 2015 to equal the record for a single tournament held by Jonah Lomu and Bryan Habana. He has scored two hat-tricks among that haul, including one in the quarter-final victory over France.
The nominees were selected by an independent World Rugby Awards panel, chaired by Australia's Rugby World Cup 1999-winning captain John Eales.
The panel has deliberated on every major test played in 2015 from the Six Nations through to The Rugby Championship, World Rugby Pacific Nations Cup and Rugby World Cup 2015, with additional emphasis placed on matches at rugby's showcase tournament, before determining an average based on number of matches played to deliver a fair opportunity for all.
Following a stellar year of rugby there were a number of players representing a broad range of nations on the cusp of the shortlist.
Eales said: "This has been a very special year for rugby with some outstanding individual and team performances. Through voting and consultation the panel has concluded six worthy finalists for the Player of the Year award. Being a World Cup year, particular weighting has been given to World Cup performances, where there are four candidates who will contest the final on Saturday."
Previous winners include Brodie Retallick, Kieran Read, Thierry Dusautoir, Bryan Habana, Jonny Wilkinson and Richie McCaw, the All Black captain the only player to receive the award more than twice.
The World Rugby Player of the Year 2015 is one of 13 categories of awards, including the World Rugby Team of the Year, World Rugby Coach of the Year, World Rugby Sevens Player of the Year in association with HSBC, World Rugby Women's Player of the Year and World Rugby Breakthrough Player of the Year.
The awards will be presented at the World Rugby Awards in London on Monday.
Previous Player of the Year Award winners:
2014 - Brodie Retallick (New Zealand)
2013 - Kieran Read (New Zealand)
2012 - Dan Carter (New Zealand)
2011 - Thierry Dusautoir (France)
2010 - Richie McCaw (New Zealand)
2009 - Richie McCaw (New Zealand)
2008 - Shane Williams (Wales)
2007 - Bryan Habana (South Africa)
2006 - Richie McCaw (New Zealand)
2005 - Dan Carter (New Zealand)
2004 - Schalk Burger (South Africa)
2003 - Jonny Wilkinson (England)
2002 - Fabien Galthié (France)
2001 - Keith Wood (Ireland)
