The 28-year-old, nicknamed The Tank, described his ''total shock'' at
discovering he had topped the poll ahead of England wing Chris Ashton and Harlequins fly-half Nick Evans.
Three days before tackling Saracens in the Premiership final, Leicester scooped an award double with Manu Tuilagi collecting the Nick Duncombe memorial trophy as young player of the year.
Tuilagi, who is banned for the Twickenham showpiece for punching Ashton in Leicester's semi-final victory over Northampton, polled 60% of the votes to finish ahead of Saints flanker Tom Wood and Saracens' fly-half Owen Farrell.
It is the second time that Leicester have taken both prizes at the RPA
Computacenter Rugby Players' Awards, after Martin Corry and Harry Ellis completed the prestigious double in 2005.
"It's a huge honour to have won the Computacenter Players' Player of the Year award and it has capped a great first season for me in the Premiership,'' said
Waldrom, who was also voted the Leicester supporters' player of the year.
"I know it's always said, but being voted for by your fellow players really is
a big deal. There's no greater compliment and I'd like to thank the players who voted for me.
"It was a total shock when I found out because there are so many fantastic players in the Premiership who could've won it. I was happy just to make the nominees list.
"It's amazing to be seen in the same league as a player like Nick Evans who was also on the shortlist. I personally voted for Tom Wood. He puts in a tremendous amount of work and I think he's had a wonderful season.
"When I first arrived here my expectations were to play a few games here and there, but due to a few injuries I got a run of games and was able to build on that.''
Waldrom will be visiting Twickenham for the first time in his life for the
Premiership final on Saturday and he has eyes on making England's World Cup squad after discovering earlier this season he has an English grandparent.
"It's the first time I will have played at Twickenham - in fact it's the first
time I'll have ever been to Twickenham, so I can't wait to experience the
atmosphere there,'' said Waldrom.
"I've only ever seen it on TV so I'm really looking forwarded to running out
and seeing the stands packed with Leicester Tigers and Saracens fans.
"It's already been an unbelievable season for me. I can't believe how
fortunate I've been and if we could cap it off with a win this weekend then it would be the most memorable season I've ever had, but Saracens will have other ideas!
"Obviously I'd love to be a part of the World Cup. Who wouldn't? But I don't know whether I will be included or not. That has to wait until next week.
"I can't even think about that. All my focus has to be on the Aviva
Premiership final this weekend.
"It's all about Leicester Tigers until the end of the season. The only set
plan I have for the summer is trying to take my son to EuroDisney at some point for his birthday!''
Tuilagi was also voted Premiership young player of the year and he has been tipped for a place in England's World Cup squad after a remarkable breakthrough season.
"I'd like to thank all the players who have voted for me. It is a big honour
and I am humbled to win this award,'' he said.
Tuilagi was banned for five weeks after landing three head punches on Ashton - an episode he has apologised for and vowed to learn from.
"It is a big disappointment that the season won't finish in the way it started for me and that I won't be playing in the Premiership Final this weekend,'' the 20-year-old said.
"I'm sorry about what happened in the semi-final and I will do my best to
learn from my mistake and come back a better player.''
The HSBC special merit award was presented to retiring Bath lock Danny Grewcock while Lawrence Dallaglio was inducted into the LV Hall of Fame.
The Blyth Spirit Award went to Leeds' James Tincknell for "his inspiring
progress after a life-threatening car crash''.
Bath scrum-half Michael Claassens won the Sunday Times try of the year for his effort against Exeter.
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