Desmond Mills Jr, 33, originally pleaded not guilty, but switched to take a plea bargain from prosecutors. He is the first of the officers to face sentencing in Mr Nichols' killing.
He will face up to 15 years in prison, according to authorities.
Mr Nichols, 29, was beaten by several Memphis police officers for approximately three minutes on 7 January. The incident was captured on surveillance video and by police body cameras.
While he survived the initial attack, Mr Nichols died three days later in the hospital.
Mr Mills and four other former officers — Emmitt Martin III, Tadarrius Bean, Demetrius Haley and Justin Smith — were indicted on federal charges for use of excessive force and for violating Nichols' civil rights. They were also charged with conspiring to make false statements to their supervisors and for obstructing justice during subsequent investigations, according to the Washington Post.
The four other officers involved in the case have pleaded not guilty to their charges. All five have pleaded not guilty to Tennessee state charges of second-degree murder.
Mr Nichols' death prompted widespread outrage, sparking protests and driving a Justice Department investigation into the culture, training, and policies of the Memphis Police Department.
The incident resulted in the dismantling of the department's "Scorpion" unit, which was tasked with investigating drug cases. All of the officers involved in Mr Nichols' death were assigned to the Scorpion unit.
The charges also resulted in the Shelby County District Attorney Steven Mulroy tossing out charges in 30 cases that the implicated officers investigated. Charges were reduced in a dozen other cases.
“Desmond Mills’ plea today is entirely consistent with our allegations in the civil lawsuit against the City of Memphis,” Ben Crump and Antonio Romanucci, the attorneys representing Mr Nichols' family, said in a statement. “We stand strong in our belief that these officers, including Mills, acted at the direction of a policy that not only violated civil rights of innocent civilians but which caused needless pain to many.”