He choked back tears as he told her: "I didn't want to steal anything from anyone. ... I'm sorry, sorry."
Simpson said he was simply trying to retrieve sports memorabilia and other mementos, including his first wife's wedding ring, from two dealers when he stormed a Las Vegas hotel room on Sept. 13, 2007.
But the judge emphasized that it was a violent confrontation in which at least one gun was drawn, and she said someone could have been shot. She said the evidence was overwhelming, with the planning, the confrontation itself and the aftermath all recorded on audio or videotape.
Glass, a no-nonsense judge known for her tough sentences, imposed such a complex series of consecutive and concurrent sentences that even many attorneys watching the case were confused as to how much time Simpson got.
Simpson could serve up to 33 years but could be eligible for parole after nine years, according to Elana Roberto, the judge's clerk.
The judge said several times that her sentence in the Las Vegas case had nothing to do with Simpson's 1995 acquittal in the slaying of his ex-wife Nicole Brown Simpson and her friend Ronald Goldman.
"I'm not here to try and cause any retribution or any payback for anything else," Glass said.
Simpson was immediately led away to prison after the judge refused to permit him to go free on bail while he appeals.
Simpson's co-defendant and former golfing buddy, Clarence "C.J. Stewart, also was sentenced to at least 15 years.
Outside court, Goldman's father, Fred Goldman, and sister, Kim, said they were delighted with the sentence.
"We are thrilled, and it's a bittersweet moment," Fred Goldman said. "It was satisfying seeing him in shackles like he belongs."
The Goldmans took a measure of credit for Simpson's fate, saying their relentless pursuit of his assets to satisfy a $33.5 million wrongful-death judgment "pushed him over the edge" and led him to commit the robbery to recover some of his sports memorabilia.
Simpson and Stewart were both brought to the courtroom in dark blue jail uniforms, their hands shackled to their waists with chains. Simpson, who looked weary and had not been expected to speak, delivered a somber statement to the judge.
As he spoke in a hoarse voice, the courtroom was hushed. His two sisters, Shirley Baker and Carmelita Durio, sat in the front row of the courtroom, along with his adult daughter.
Both men were convicted Oct. 3 of 12 criminal charges, including kidnapping and armed robbery.
"As stupid and as ill-conceived as it was, it wasn't something that was from this evil mind they teach us about," Simpson attorney Yale Galanter said before sentencing.
"Not bright, not smart, not well thought out, but certainly not from an evil mind," Galanter said.
Most of the 63 seats in the courtroom were taken by media, lawyers and family members of the defendants. Fifteen members of the public were also allowed.
After sentencing was over, the Goldmans left the courtroom and Kim threw her arms around her father and wept.
Simpson's sisters declined to comment, but Shirley Baker said on her way out: "It's not over."
Jurors who heard 13 days of testimony said after the verdict that they were convinced of Simpson's guilt because of audio recordings that were secretly made of the Sept. 13, 2007, robbery at the Palace Station casino hotel.
The confrontation involved sports memorabilia brokers Alfred Beardsley and Bruce Fromong. It was recorded by collectibles dealer Thomas Riccio, who was acting as middleman.
"Don't let nobody out of this room!" Simpson commands on the recordings, and instructs other men to scoop up items he insists had been stolen from him.
On Tuesday, Glass is scheduled to sentence four former co-defendants who took plea deals and testified against Simpson and Stewart.
Michael McClinton, Charles Cashmore, Walter Alexander and Charles Ehrlich could receive probation or prison time. McClinton could get up to 11 years; the others face less.
AP Special Correspondent Linda Deutsch contributed to this report.