Bourque was charged Friday night with operating under the influence of alcohol and following too closely. He posted bail and was released.
"For the first time in my life, I find myself in unfamiliar territory," Bourque said in a statement released Sunday. "I am not happy about the situation I put myself into."
Andover Police Chief Patrick Keefe said the 55-year-old Bourque was arrested about 11:30 p.m. after his Mercedes-Benz rear-ended a minivan in a construction zone in the city. No injuries were reported.
"I am a very proud person that accepts the responsibility of my actions and have always accepted being in the media eye," Bourque said. "I have used this popularity to try and positively impact as many lives as possible. I am happy that no one was hurt in the accident and thank everyone who has reached out in support of my family and me."
Bourque is to be arraigned in Lawrence District Court. Police haven't provided a date.
According to The Boston Globe, Bourque owns Tresca, a restaurant on Boston's North End.