Handley, 23, received his honour - sponsored by Tetley's - at Rhinos' awards night on Monday.
Fellow winger Tom Briscoe was runner-up, with captain and loose-forward Trent Merrin in third place.
Rhinos' seven-time Grand Final winner Carl Ablett has announced his retirement.
The 33-year-old, who has made more than 300 appearances for the club since his debut in 2004, has not played this year due to an ankle injury.
Ablett and Jamie Jones-Buchanan, who is also retiring at the end of the season, received special presentations.
Young centre Harry Newman is Rhinos' Yorkshire Evening Post Shooting Star for 2019.
The teenager received the award from YEP competition winner David Muhl.
He came top in a vote of Evening Post readers for the young player, aged under-24, who has made the biggest impact this season.
Runners-up were Mikolaj Oledzki and Cameron Smith.
Konrad Hurrell, in his first season at the club, was named Kong Media fan's player of the year.
The Chris Sanderson Memorial Trophy for academy player of the year,sponsored by 15ten15, which went to Sam Walters.
Head groundsman Ryan Golding was named clubman of year.
Leeds Building Society try of the year was won by Rhyse Martin for his touchdown against Catalans Dragons. Second was Konrad Hurrell at Hull KR and Richie Myler against Catalans was third.
Other nominations were Ash Handley v Salford, Hurrell v Huddersfield Giants, Tom Briscoe v Huddersfield and Jack Walker v Castleford.
There will be a page of pictures from the awards presentation in Wednesday's Yorkshire Evening Post and online.