The 38-year-old former fugitive Rudolph bombed a gay nightclub and two other family planning clinics and intended to bomb other targets, prosecutors said.
Rudolph, who was on the run for five years until his capture in 2003, killed two people and injured more than 120 injured with his nail bomb blasts.
“Once we identified Rudolph and had him on the run, the bombings ended, saving who knows how many lives,” said US Attorney David Nahmias.
Rudolph released a rambling, right-wing statement, which for the first time, offered a motive for the attacks.
He said he targeted the Games to embarrass the US government in front of the world “for its abominable sanctioning of abortion on demand” and expressed remorse for the bombing.
“I do apologise to the victims and their families” he wrote, adding he intended only to target “agents of the Washington government” or “abortionists.”
He firstly appeared before Atlanta federal Judge Charles Pannell and pleaded guilty to the 1996 bombing of Olympic Park, in which one woman was killed and 111 people injured.
He admitted he’d planned a much larger attack that would’ve used five bombs over several days that would’ve left “only uniformed arms-carrying government personnel exposed to potential injury.”
But he said poor planning on his part made that five-bomb plan impossible.
As part of his guilty plea, prosecutors agreed to drop the death penalty. Instead, the serial bomber will be sentenced to multiple terms of life in prison without parole
He also told authorities where he had hidden more than 113 kg of dynamite, including a fully built bomb.
“I have deprived the government of its goals of sentencing me to death,” Rudolph said the statement. “The fact that I had entered an agreement with the government is purely a tactical choice on my part and in no way legitimates the moral authority of the government to judge this matter or to impute guilt.”
He faced another court hearing in Birmingham, Alabama, over the abortion centre bombings.
At this hearing, Rudolph winked at prosecutors as he entered court, said the government could “just barely” prove its case, and admitted his guilt with a hint of pride in his voice.
Rudolph never made eye contact with the victims in the Alabama court and appeared to show no remorse.
He said he understood his rights but did not explain during the one-hour hearing why he had carried out the blasts.
When asked by the judge if he planted the bomb outside the abortion clinic which killed a policeman he replied: “I certainly did your honour.”
Sentencing in both courts is scheduled for July 18, the birthday of Emily Lyon, the nurse wounded in the abortion clinic blast.
At the height of efforts to catch Rudolph, US officials fielded 250 federal agents, sniffer dogs and heat-seeking helicopters to flush him out of the North Carolina Mountains.
Federal officials said sympathisers in the area had protected Rudolph as a crusader and helped him elude authorities.
In May 2003, a policeman caught Rudolph sifting through garbage behind a food store.