The three-year-old French bulldog was entered into the annual competition, which promotes responsible dog ownership, before the MP was stabbed to death in his constituency earlier this month.
As part of the entry, Sir David had said Vivienne “lifts my spirits as she is always pleased to see me and she makes me smile”.
He added: “Every time I walk into the room Vivienne throws herself at me, lies on their back with her legs in the air to be tickled.
“But before that she always brings a toy so she is of a generous, giving nature.”
The Southend West MP described himself as a “great animal lover” on his website, something that was reflected in his record in Parliament.
He was responsible for introducing the Protection Against Cruel Tethering Act in 1988, campaigned to stop the testing of domestic products on animals, tackled the illegal wildlife trade and fought for an end to puppy farming, according to his website.
He opposed the culling of badgers and was one of the few Tory MPs in favour of a foxhunting ban.
In his most recent Commons intervention, on September 23, he called for a debate on “animal welfare generally, cruelty to animals and the welfare of farmyard animals” to mark World Animal Day on October 4.
The Tory veteran was a patron of the Conservative Animal Welfare Foundation and won the Dods Animal Welfare and Environment Award in 2011 for his work on the issue.
He also regularly judged at local dog shows and supported various local animal charities.
MPs had been urged to vote for Vivienne in the competition, with Conservative MP Andrew Rosindell telling the Commons earlier this week that there could be no better tribute to Sir David.
He told MPs: “As our dear friend David Amess said in June about the Kept Animals Bill: ‘I hope the House will come together, support the Bill, and get it quickly onto the statute book’.
“I could think of no better tribute to him and to the animals across the United Kingdom which he so adored.”
The deputy speaker Nigel Evans said: “I think one thing is absolutely certain, that had the tragedy not befallen David recently he would have been in this debate today championing animal rights, which was so close to his heart.”
Mark Beazley, chief executive of The Kennel Club, which organised the competition alongside the Dogs Trust, said: “Whilst the competition itself is no doubt a light-hearted and fun event, it is also an excellent opportunity to showcase the happiness that dogs can bring to our lives and to raise awareness of the actions that need to be taken, both in Parliament and beyond, to promote responsible dog ownership.”
Sir David, 69, was stabbed to death at Belfairs Methodist Church in Leigh-on-Sea in Essex on October 15. His funeral is to be held at Westminster Cathedral on November 23.
Ali Harbi Ali, 25, has been charged with terrorism offences and murder.
He faces a trial in March next year.