The 51-year-old replaces Jack Ross, who was sacked by the Black Cats on 8 October after winning five of their first 11 League One games this term.
Parkinson spent three years in charge of Bolton, winning promotion to the Championship in his first season.
He resigned as manager in August, with Wanderers bottom of the third tier after being deducted 12 points.
"It is both a privilege and immense responsibility to be appointed manager of this great club," Parkinson said.
"This is a good squad of players, and I relish the challenge of working with them to achieve our goal of promotion from League One."
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