New York City plans to build a three-mile-long tunnel to divert water from a leaking aqueduct that carries from the Catskills about half of the city’s drinking water, officials announced on Friday.

The tunnel, to be built under the Hudson River and parts of Dutchess and Orange Counties, will address a problem that has daunted the city since leaks were first discovered in the Delaware Aqueduct in 1988: some 15 million to 35 million gallons of water, coming down from the Catskills, have been escaping daily through cracks.

The tunnel will bypass the worst of two leaks, said Caswell F. Holloway, the city’s environmental commissioner. Construction work is expected to begin in 2013 and be completed by 2019 at a cost of about $1.2 billion, officials with the city’s Department of Environmental Protection said. Officials said that cost, spread out over nine years, was built into the department’s capital program.

For years, the city has faced criticism for its long delays in stanching leaks in two sections of a 45-mile stretch of the aqueduct known as the Rondout-West Branch tunnel, in Orange and Ulster Counties. The cracks in that branch, which was completed in 1944, have caused chronic flooding in the Ulster hamlet of Wawarsing.