Prosecutors alleged Mejia-Ramos stabbed his wife Deisy Garcia to death, then hugged and kissed his two young daughters before setting them down on their bed and killing them too.
Miguel Mejia-Ramos was arrested Monday in Texas after authorities tracked his cellphone.
A man suspected of killing his wife and their two young daughters in New York City has waived extradition from Texas.
Miguel Mejia-Ramos, 28, was captured early Tuesday morning at a vehicle roadblock in Schulenburg, Texas, located between Houston and San Antonio, the NYPD said.
Police say 21-year-old Deisy Garcia, 2-year-old Daniela Mejia and 1-year-old Yaslin Mejia were found dead in an apartment in Jamaica Sunday night.