Rajeswari, 43, who had immigrated to the US from India as a teenager, previously worked with the Richmond County District Attorney's Office for her entire career in several bureaus including Criminal Court, Narcotics, Supreme Court, and the Sex Crimes Special Victims Bureau, where she last served as deputy chief.
Rajeswari took the oath of office at a ceremony in New York on Monday along with 27 other judges appointed earlier this month to the Family Court, Criminal Court, and Civil Court, which are part of the New York State Unified Court System.
The mayor appoints judges to 10-year terms in the New York City Criminal Court and the Family Court within the city.
"To ensure New Yorkers have access to a fair, equitable justice system, we need judges who are qualified, honest and reflective of the people of this city," said Mayor de Blasio.
"With their wealth of legal experience, these appointees represent all five boroughs and all walks of life. From the first female South Asian-American judge in New York City to a former NYPD First Deputy Commissioner, these talented leaders truly reflect the diverse range of communities that make up our great city," he said.
The mayor said Rajeswari has an "extraordinary, extraordinary empathy for others."
He lauded her ability to speak in Indian, Middle Eastern and Southeast Asian languages, saying she put her history as an immigrant and ability to speak all these languages to work, "helping to reach immigrants" in the Staten Island communities where she served as an Assistant District Attorney.
"And she saw as her mission to give them confidence in the justice process," de Blasio said.
Rajeswari had said in a report earlier this month that she is "honoured and humbled" by her appointment.
"It's like a dream. It's way beyond what I imagined," she was quoted as saying in the media report.
"For someone like me, an immigrant who comes from India, I'm beyond grateful," she said.
"I told the mayor this is not only my American Dream, but it shows another girl from a far away country that this is possible," Rajeswari had said.
Rajeswari has served in the district attorney's office for the past 16 years and has been the deputy chief of the Special Victims Unit for more than four years.
She has worked on cases involving women and children and said they are the ones that touched her the most.
Rajeswari said that she hopes to use her new position to improve the judicial system by encouraging interpreters to have more access to aid immigrants.
"I'm honoured to sit on a city bench and make Staten Island proud," she said.