Under the agreement approved by Montgomery County state District Judge Kelly Case and announced during a scheduled court hearing, Peterson pleaded no contest to a misdemeanor charge of reckless assault.
Case deferred a finding of guilt for two years while imposing a $4,000 fine and 80 hours of community service on Peterson.
"I'm just glad this is over," Peterson said shortly after Tuesday's plea deal was announced. "I can put this behind me, and me and my family can move forward."
Peterson was indicted in September on a felony charge of injury to a child for using a wooden switch to discipline his 4-year-old son earlier this year in suburban Houston. The All-Pro running back says he never intended to harm his son and was disciplining him in the same way he had been as a child growing up in East Texas.
The boy suffered cuts, marks and bruising to his thighs, back and on one of his testicles, according to court records. If convicted of felony child abuse, Peterson could have faced up to two years in prison and a $10,000 fine.
"I truly regret this incident," Peterson said. "I take full responsibility for my actions. I love my son more than anyone you could even imagine, and I'm anxious to continue my relationship with my child."
The NFL and the Vikings have not yet announced whether they will suspend Peterson, who already has missed eight games with pay this season under the terms of the commissioner's exempt list.
League spokesperson Brian McCarthy did not offer a timetable for when the NFL will make a decision, telling ESPN's Ben Goessling that the league "will review the court documents."
Last month, a visiting judge denied a request by prosecutors to remove Case as judge in the case. Prosecutors had accused Case of being biased against them and wanted a new judge appointed.
The plea deal made moot a pending motion by prosecutors to revoke Peterson's $15,000 bond for alleged marijuana use.
The NFL Players Association expects that the league will punish Peterson as it would any other player determined to be guilty of a misdemeanor, league sources told ESPN's Ed Werder.
The union will likely argue, sources told Werder, that Peterson, who has been paid his full salary of nearly $5.3 million in his absence, should be reinstated and perhaps forced to pay a substantial fine. Only commissioner Roger Goodell can reinstate Peterson from the exempt list, meaning the two could be required to meet.
Both players agreed as part of a deal that they would be ineligible to play until their cases are adjudicated, but that they would receive full compensation until that time.
Once Goodell reinstates Peterson, presuming the commissioner eventually does so, the Vikings would either have to allow the running back to return to the team or be required to release him.
Vikings general manager Rick Spielman declined to comment on Peterson during his midseason news conference Tuesday.
"All I'm going to say is basically at the appropriate time, and I know you guys can appreciate this, we'll keep all of our comments under the Adrian situation until it's appropriate to speak," Spielman said. "And I'll just leave it at that."
"We all know the kind of person he is. We've stood behind him this whole time. You'd be crazy not to welcome him back into that locker room. It would be a big pickup for this locker room being we have so many young guys."
Vikings tight end Kyle Rudolph, on teammate Adrian Peterson
Vikings coach Mike Zimmer was asked about Peterson on Monday as the team began its bye week, and he made it clear he judges Peterson based on his own personal interactions and considers him to be "top-notch, first-class."
Several prominent Vikings players said Tuesday they'd be excited to have Peterson back on the roster, adding that the running back wouldn't have to do anything to regain trust in the locker room.
"We all know the kind of person he is," tight end Kyle Rudolph said. "We've stood behind him this whole time. You'd be crazy not to welcome him back into that locker room. It would be a big pickup for this locker room being we have so many young guys. Any time you can have a veteran back in that locker room, the leader that he is in the locker room, out on the practice field, would be huge for us.
"Guys have chatted amongst each other, and I don't think there's anyone in that locker room that would need to hear from him. We all know the kind of person Adrian is, and I feel like he's proven that over his time here."
A prolific player at his position, Peterson set an NFL record with 296 rushing yards against San Diego on this date in 2007.
The case revived a debate about corporal punishment, which is on the decline in the U.S. but still widely practiced in homes and schools.
Corporal punishment is legal in every state. The Texas Attorney General's office notes that belts and brushes "are accepted by many as legitimate disciplinary 'tools,'" but "electrical or phone cords, boards, yardsticks, ropes, shoes, and wires are likely to be considered instruments of abuse."
Texas law says the use of non-deadly force against someone younger than 18 is justified if a parent or guardian "reasonably believes the force is necessary to discipline the child or to safeguard or promote his welfare."
Information from ESPN's Ed Werder, Michele Steele and Ben Goessling and The Associated Press is included in this report.