Paris Hilton has reached a plea agreement with prosecutors in her drunk-driving case, PEOPLE has learned.

Hilton entered a plea of no contest Monday to a lesser charge of reckless driving and was placed on 36 months probation. She must also pay a fine of $390 and attend an alcohol education program.

"I just spoke with Paris an hour ago, and she's happy the matter is behind her," Hilton's rep, Elliot Mintz, tells PEOPLE.

"We believe this was an appropriate resolution given the facts in this matter and both sides' desire to avoid a trial on the original charges," says Hilton's attorney, Howard Weitzman, who is also representing Nicole Richie in her pending DUI case.

Two weeks ago, the heiress pleaded not guilty to two misdemeanor counts of DUI and driving with a blood-alcohol level of .08 or higher.

Hilton, 25, was arrested Sept. 7 just after midnight for driving erratically in her silver Mercedes-Benz SLR McLaren in Hollywood, according to the LAPD.

She scored a .08 on a Breathalyzer, the minimum blood-alcohol level to qualify as a DUI.

Following her release from jail, she called in to Ryan Seacrest's L.A. radio show, explaining on-air that she hadn't eaten anything all day and was on her way to a fast-food restaurant when she was pulled over.