Want a cat or dog, but live in Queens or the Bronx? Soon, you won’t have to go to Long Island, Brooklyn or Manhattan to adopt one.

More than 14,000 cats and dogs abandoned or found every year in Queens and the Bronx end up transported to shelters in other counties. Now, they’ll get the care they need, and a place to stay, closer to home.

Among the many nuggets in Mayor Bill de Blasio’s budget, the $10 million to open full-service animal shelters in Queens and the Bronx may seem insignificant. But it’s not.

It’s an idea that’s long overdue and deserves City Council support. The shelter system has been broken for years. The lack of facilities in these two boroughs has resulted in overcrowding in existing shelters. It’s also more difficult for Queens and Bronx residents to find lost pets, because their animals end up in other boroughs and are hard to track. And it requires quite a trip for those who wish to adopt a pet.

The new shelters were backed by NYCLASS, the same group that pushed for the ill-fated de Blasio-backed ban on carriage horses. NYCLASS financed a campaign against de Blasio’s foe in the 2013 Democratic primary, Christine Quinn, and supported Campaign for One New York, a nonprofit organization linked to the mayor that’s now part of investigations into his campaign’s fundraising efforts.

This cause is a good one, no matter where the initial push came from. But there is a problem. The $10 million isn’t enough; officials estimate it’ll take more than $30 million total to build both shelters. The city should make sure the shelters are fully funded and open as soon as possible. It will be important to find the right sites in locations that are accessible to as many borough residents as possible. They’ll require the staff, operating budget and oversight to succeed. City officials must see this through.

A truly citywide animal shelter system can provide a home for the many pet pit bulls, poodles, cats, rabbits and birds found in every borough. It’ll not only help the animals, but also the humans who want to care for them.

See photos dogs and cats found in Queens and the Bronx, but unavailable for adoption there: amny.com/opinion