Proposed by Conservative MSP Maurice Golden, the Dog Abduction (Scotland) Bill received full support from 92.4% of the 237 responses, while a further 4.2% were partially supportive.
If passed, the Bill will create a specific crime of dog theft punishable by up to five years in prison.
Among those backing the Bill was the Scottish SPCA, Dogs Trust, OneKind, Battersea Dogs and Cats Home and Canine Concern Scotland.
The Bill will now be lodged at Holyrood where it will seek support from MSPs in order to be introduced and potentially become law.
Mr Golden said: “The results of this consultation confirms the public’s appetite to tackle this appalling crime.
“The theft of a dog is among the most traumatic things that can happen to an owner, and as it stands the law simply doesn’t do them justice.
“The law also doesn’t do enough to deter thieves, to support police in tracking them down or to build a robust picture of the scale of the problem.
“My proposed Bill aims to address all of that.
“The overwhelming support is hugely encouraging, both from the public and widely-respected animal welfare organisations.
“I also thank those who aren’t convinced and have concerns – we very much want their help in creating this legislation too.
“MSPs from all parties in Holyrood have expressed support for this, and I look forward to working on a cross-party basis to move this proposed Bill to the next stage.
“It’s been long said dogs are people’s best friend – it’s time the law in Scotland gave them the status and protection they deserve.”
In its response, the Scottish SPCA said: “Dogs are seen as family members and losing a pet to theft is devastating for owners and for the pet. The society sees the immense value in the human-animal bond and the benefits the relationship can have on both people and pets.
“When a dog has been stolen this does trigger a traumatic experience for owners with expectation of police support rarely met, resulting in victims physically searching themselves, moving from local searches to regional and national searches.
“The Scottish SPCA does not believe a price should be placed on an animal to determine the punishment for theft, or on the love between a person and their dog.”
Iona McGregor, whose two cocker spaniels were stolen, said it was “utterly devastating”, adding: “If there was a firm punishment in place these sorts of crimes would be less likely to occur.
“That is why we strongly feel that this dog theft Bill should be passed.”
The Law Society of Scotland said it is not opposed to the creation of a new offence but will require more evidence to prove there is a need for it.