Rice, 25, admitted two felony counts of collision involving serious bodily injury and racing on a highway causing bodily injury, the Dallas County District Attorney's Office said.
The Chiefs ace, a member of Kansas City's 2023-2024 Super Bowl-winning team, left the scene of the crash in Dallas on March 30 last year after racing in his Lamborghini at speeds of up to 119 miles per hour (191 kilometers per hour).
Dallas prosecutors said Rice had made "multiple aggressive maneuvers" which led to the crash causing a "chain reaction that affected multiple vehicles." Rice fled the scene of the crash on foot.
As part of his plea agreement, he was ordered to pay just under $115,500 toward victims' medical expenses.
In a statement released through his attorney, Rice apologized to his victims.
"There have been a lot of sleepless nights thinking about the damages that my actions caused," Rice said.
"I am profoundly sorry for the physical damages to person and property. I fully apologize for the harm I caused to innocent drivers and their families."
Dallas County District Attorney John Creuzot said it had been "extremely fortunate that no lives were lost that day".
"And Mr. Rice is fortunate to have walked away unharmed," Creuzot added.
"We hope he takes this as an opportunity to mature and leads by example moving forward."
US media reports said Rice would be able to serve his 30-day prison term at any point during the five years of his probation.
With criminal proceedings concluded, the receiver is now likely to face a hefty multi-game suspension from the NFL for violating the league's personal conduct policy.