The Irishman, who made his 500th appearance for United against Luton in February, was presented with his award by trophy sponsor Alan Haysom of Jackson Trophies in Cross Gates.
Jackson's have sponsored the award since 2002 when Rio Ferdinand became the first YEP readers' player of the year.
Mark Viduka won the award the following season, following a late goal flurry that kept United in the Premiership, while Alan Smith was the recipient when Leeds suffered relegation in 2004.
Last season's winner was Neil Sullivan, by a landslide, but the voting was closer this time around. Kelly polled the most, while Shaun Derry's performances in midfield also garnered plenty of support from our readers.
Other votes were cast for Eddie Lewis, Paul Butler, Sullivan, David Healy, and Sean Gregan, but it was Kelly who pipped Derry to the honour.
The 31-year-old has missed just one Championship game this term and also ended his near three-year drought in front of goal when he scored a stunning late equaliser against Wigan in the FA Cup third round replay at Elland Road.