The debate will take place in Brooklyn and will be moderated by CNN anchor Wolf Blitzer, who led two GOP debates earlier this election season.
CNN chief political correspondent Dana Bash and NY1 political anchor Errol Louis will join in the questioning of the candidates.
Time Warner Cable News NY1 is the main 24-hour cable news channel in New York City. Both CNN and NY1 will carry the debate live from 9 p.m. to 11 p.m. Eastern.
The announcement ends days of back-and-forth between the two campaigns about exactly when and how to debate in advance of the New York primary.
The Sanders campaign originally called for a Democratic debate in New York months ago. But narrowing it down to an exact date proved difficult.
The Sanders and Clinton campaigns sparred in private and in public about what date and time was best.
Over the weekend the Clinton campaign focused on the April 14 date, and Sanders made clear he wanted a debate in Brooklyn.
Sanders had also cited his campaign's plans for a major rally in Washington Square Park that evening.
On Monday the city's mayor, Bill de Blasio, a Clinton supporter, sought to ease the way forward.
"Let's make @NY1 4/14 BKLYN debate happen," he tweeted. "@BernieSanders: I'll help you secure any permit you need to ensure your NYC rally can happen too."
It will be held at the Duggal Greenhouse on the Brooklyn Navy Yard, the borough where Sanders was born and where Clinton has her campaign headquarters.
The two candidates have not debated on stage since the Univision-Washington Post debate on March 9.
The Democratic National Committee has sanctioned the CNN-NY1 debate.