"These have been very, very sad time for everybody; for them, for us, and I hope it's finished soon for everybody," Vargas' mother Xiomara Vargas said.
Xiomara and Manual Vargas traveled from their home in Mexico City to hear their son plead guilty.
"We are very, very sorry for what has happened to the Mr. White's family, for Ryan White," Xiomara said.
Andrew Vargas, 22, agreed to the plea, which calls for a year in jail and five years on probation.
Both sides said it was a fair deal.
"Andrew is not a horrible person but he made a horrible mistake," assistant district attorney Omid Talai said. "There are consequences for those actions."
"Andrew felt terribly with what he had done and he wanted to take responsibity for his actions," defense attorney Randall Knox said.
Ryan White was critically injured last August after he and his family watched the Phillies beat the Giants at AT&T Park. They were visiting from Philadelphia. A Toyota pickup driven by Vargas hit White as he walked across the street at Mission and New Montgomery streets. Vargas' pickup then plowed into several cars as he fled the scene.
The driver of a taxi that was one of the cars Vargas sideswiped chased Vargas for a few minutes before losing him, but other witnesses gave investigators the license plate number. Officers from Hayward spotted the damaged Toyota and Vargas was arrested after a field sobriety test showed he was drunk.
Talai says the plea would not have happened if White's parents were not 100 percent on board.
"With this agreement, we have their blessing for this plea today," Talai said.
Vargas has been in jail this whole time, but he will get credit for time served.
White is doing better and is back to attending school part time.