All dogs in England, Scotland and Wales are now legally required to have been chipped by the time they are eight weeks old.
The government says one million dogs - about one in eight of the estimated UK dog population - are not yet chipped.
Animal welfare minister George Eustice said: "We are a nation of dog lovers and we want to make sure they stay safe.
"Not only will this mean the UK's 8.5 million dogs can be returned to their owners more quickly if they wander too far from home, but it will also make it easier to track down the owners of dogs that carry out attacks on people," Eustice said.
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"Microchipping our dogs will not only reunite people with their lost or stolen pets, but also help to tackle the growing problem of strays roaming the streets and relieve the burden placed on animal charities and local authorities."
When a dog is microchipped, a tiny chip about the size of a grain of rice is inserted under the loose skin on the back of its neck, giving it a unique 15-digit code.
If a dog is lost or gets stolen and is picked up by a council or a dog shelter, the microchip can be scanned and matched to contact details stored on a database.
Charities such as the Dogs Trust, some local authorities and some vets will microchip dogs without charging.
The new law will not replace current requirements for dogs to wear a collar and tag with their owner's name and address when in a public place, Defra said.
Figures from the Dogs Trust indicate that the number of stray dogs in the UK has been in decline since 2011.
An estimated 102,363 stray dogs were handled by local authorities in the year from April 2014, compared with 126,000 in 2011-12, it said.