One tradition started by Arpaio, making inmates wear pink underwear, has already been slowly phased out.
Tent City was the location of a 1996 riot by hundreds of inmates.
Critics say the complex was a way for Arpaio to garner media attention.
But it also cast a dark mark on Phoenix and attracted criticism from civil rights groups who called Arpaio's methods needlessly harsh.
Last November, voters in Maricopa County, Arizona, finally ousted "America's Toughest Sheriff" Joe Arpaio from office.
Paul Penzone, a Democrat and retired Phoenix police sergeant, was elected on the promise of rolling back existing law enforcement policies he viewed as purposeless and self-aggrandizing.
Penzone projected that at least half of the tent population will be moved indoors within 45-60 days.
File image of immigrant inmates showng off a pair of pink underwear while sitting on a bunk in the Maricopa County Tent City jail on March 11, 2013 in Phoenix, Arizona.
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The tents created this ovenlike effect so even though they were open air, the temperature inside them would somehow climb higher than the outside temperature, sometimes higher than 130 degrees.
"This facility became more of a circus atmosphere for the general public". "Starting today, that circus ends and the tents come down". "It is not cost effective and it is not tough on criminals", Penzone said. But that's just a projection, we'll stay on the story and keep you updated on what kind of effect this actually has on the sheriff's budget. As Sheriff, Arpaio led a profiling sting in his county, requiring officers to racially profile drivers in the hopes of arresting undocumented immigrants.
Incarcerated nonviolent convicts - many of whom were found guilty of drug possession, driving under the influence, or domestic violence charges - were often subjected to beatings or had health conditions exacerbated by the hot Arizona sun, leading to deaths in certain cases.
During the news conference, Penzone said at least half of the people now detained at Tent City will be moved to secure facilities, within the first 45 to 60 days after the announcement Tuesday. He assembled an advisory committee with members from across the political spectrum to conduct a "methodical review" of the economic and safety challenges at Tent City.
Penzone said the closure would save taxpayers $4.5 million.
"I think he's insulting all the circus people", said Arpaio, referencing Sheriff Penzone's quote that the "circus ends". He said there was no data to show that the facility deterred crime.
Tent City has the capacity of holding 2,100 inmates and peaked at 1,700 inmates, former Arizona Attorney General Grant Woods said at a news conference. "Not mine. I'm not going to second-guess him", he said.
Penzone stressed that the safety of MCSO's employees was a major part of his decision, which came after a review by the SPEAR Board tasked with determining the facility's effectiveness.