Peck says his exit is a mutual decision, telling us ... "After filming 13 great seasons of Ink Master, the producers and I have decided it’s best to part ways." He also acknowledged the blackface pics, saying, "The offensive photos of me which recently surfaced from many years ago can only be a distraction to the amazing show I have loved being a part of and its many talented artists."

He ended on a conciliatory note, saying ... "I want to thank the show’s cast, crew, contestants and awesome fans. It’s been a blast and an honor and I wish my friends and colleagues the very best in whatever the future holds." He's been on as a judge since 2012.

Peck's now ex-employers at Paramount Network also denounced the scandal, saying ... "We, like many others, were appalled when we saw the photos of Oliver. We were glad to see his apology and accept that he is taking full responsibility for the damaging impact of his actions."

You'll recall ... photos of Oliver in blackface surfaced a week ago, some of which were posted to his old MySpace page. In one photo, you could see him applying dark makeup to his face and upper body, and went on to dress in blackface costumes at least twice.

Many people were calling for his job on "Ink Master," and it looks like they got what they wanted -- but there's a catch ... he WILL still appear on the show's upcoming 13th season.

Sources connected to the production tell us this latest installment has already been shot with Oliver appearing, and will air as it was recorded, and on schedule, starting Tuesday night.