The 15-week-old Jack Russell cross has moved into the flat above No. 11 where the new prime minister and his girlfriend live.
Ms Symonds revealed the pooch’s name – Dilyn – on Twitter along with adorable pictures of him exploring his new home.
The puppy was rescued by Eileen Jones, who runs the animal refuge Friends of Animals Wales, after he was abandoned by dog traders.
Ms Jones, who received an anonymous tip, found the animal facing a near certain death, having suffered a misaligned jaw.
She said she often gets calls about ex-breeding dogs or puppies who are at risk and goes to meet the tipsters in lay-bys to rescue the animals.
Ms Symonds wrote on Twitter: “Thanks to the wonderful Eileen from @FOAWales who rescued Dilyn after she got a tip off that he was to be dumped by a puppy dealer because he was born with a crooked jaw. Eileen fixed his little jaw & saved his life. She is a hero.”
It thought that if the puppy had not been rescued he would have been shot.
Ms Jones, 66, brought Dilyn in a dog carrier alongside volunteer coordinators and posed for photos before he was taken inside to live in one of the most famous addresses in the world.
Plans for the adoption have been in place "for weeks", with the puppy living in a foster home with a cat to prepare him in to move in with Larry the Cat, fondly known as Downing Street's "chief mouser".
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But unlike Larry, a permanent occupant at Number 10, the puppy will belong to Ms Symonds and Mr Johnson.
The charity conducted the normal checks on Mr Johnson and Ms Symonds that everyone who is adopting a dog has to go through.
Ms Jones is carrying out a home check while dropping the puppy off today but thinks he will settle in.
“He has been living with a cat for a few weeks and from my understanding there are a lot of things in place for training. He is only a baby so he is going to be very workable and he is a delightful little pup," Ms Jones said.
“I think he will settle in well although there may be more issues on the side of the cat, but as long as the puppy learns who is boss – which will be the cat – then everything will be fine.”
She said there has been an increasing number of ex-puppy farm dogs being surrendered to the charity as a result of impending legislation known as Lucy’s Law.
Mr Johnson and Ms Symonds are keen to promote the crackdown on puppy farms, which will ban the sale of kittens and puppies from third parties from spring 2020, meaning buyers will have to deal with breeders directly.
The charity wrote in a post on its website: "We know only too well why Lucy’s Law is such an important piece of legislation because we pick up the pieces of third-party puppy selling every day.
"The suffering of these dogs is unimaginable unless you see it first-hand as we have done for so many sad years.
The statement said Ms Jones knew Ms Symonds had always been a huge animal welfare advocate.
"We are absolutely overjoyed that this gorgeous pup will be living his best life with Carrie and the prime minister at their Downing Street home,” it said.
"We wish them a lifetime of happiness with their new best friend."