The singer, 37, is most famous for being Katie Price's ex-husband.
The pair had two children, Junior and Princess, and Andre is also step-dad to Katie's son Harvey.
On winning the award, presented by Bounty, he said fatherhood was his "most important role".
He said: "This feels so good. It's been a turnaround year for me and the kids and it's an honour to be the subject of the public's support and best wishes.
"This means a huge amount to me as being a dad is my most important role."
Andre said some might say this would be the only award he would ever win. "Even if it is, what a great award to get. I mean, there isn't a better award, there isn't - because it's lifelong," he said.
"Other awards are for there and then, this is for life. My kids are going to know that I have won this."
More than 35,000 votes were cast in the poll, with Jeff Brazier, Jade Goody's partner, coming second and Take That star Gary Barlow third.
Faye Mingo, parenting spokesperson for Bounty.com said, "Bounty is thrilled Peter has been awarded the title.
"Our mums tell us that he's an inspiration for all single dads going through a tough divorce and that they respect the fact that he makes time and puts in untold effort to be able to enjoy the family life he values so much. As his career goes from strength to strength and we wish him all the best in the future."
What do you think? Would Peter Andre be your choice for Celebrity Dad of the Year?
Source: Press Association