The announcement was made by Mayor Eric Adams at his weekly briefing Tuesday morning.
He said Torres-Springer will assume the role, effective Tuesday.
"We are grateful for First Deputy Mayor Wright's years of service to the city and all she has done to deliver for children, families, and working-class New Yorkers. She is an exceptional leader who assembled a strong team and constantly demonstrated a bold vision for this city," Adams said in a statement.
Torres-Springer led ambitious and record-breaking efforts to accelerate the city's recovery from the COVID-19 and make strides against the housing and affordability crisis.
"Throughout three mayoral administrations and leading three city agencies, my focus has been to provide steady, effective leadership while delivering tangible results for every New Yorker in every neighborhood," said incoming First Deputy Mayor Maria Torres-Springer. "Serving this city has been my life's work. I am deeply grateful to Mayor Eric Adams for entrusting me with this role, and I am humbled to continue working shoulder-to-shoulder with the 300,000 public servants who work tirelessly to move our great city forward."
The news doesn't come as a surprise as sources said last week Wright was negotiating her exit from City Hall.
Wright has served in the administration since January 2022 and moved into her current role in January of 2023. She worked alongside the mayor very closely on a number of initiatives.
Last month, federal investigators seized her phones and searched her home -- along with several other officials who have since resigned.
The announcement that Wright is stepping down comes after her brother-in-law, Deputy Mayor of Public Safety Philip Banks, announced his resignation Monday.
Joining the deputy mayor leaving Monday were Winne Greco, Rana Abbasova and Mohammed Bahi.
Greco and Bahi resigned, and Abbasova was terminated. All three served as community liaisons for the administration.
Bahi was arrested Tuesday for allegedly obstructing the investigation into the mayor and his campaign. He is charged with witness tampering and destroying evidence.
Other notable names to step down from their roles previously include former police commissioner Edward Caban, outgoing school chancellor David Banks, health commissioner Ashwin Vasan, advisor to the mayor Tim Pearson, and legal advisor Lisa Zornberg.
Robert Boyce, former NYPD chief and ABC News contributor, said the City Hall shakeup is a directive from New York Governor Kathy Hochul.
"This comes directly from Governor Hochul. She said to clean house. She wants to see changes and that's what she's seeing right now," he said.
Meanwhile, David Birdsell, Kean University Provost, said many people are under the assumption that the corruption within the administration is being carried out by people with key roles.
"It looks like, right now, that administration is losing its most senior officials. At least many people believe because there is some corruption at the heart of the administration," Birdsell said.
It all comes as the Mayor continues to reassure residents across New York City that he can govern while defending himself against the federal government.
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