The forward didn't make a senior competitive appearance for the Reds during his three years on Merseyside and has now made a permanent switch to the Eredivisie side.
The 19-year-old joined the Reds from Savedalens IF in 2011 but struggled to break into the starting XI, never making a competitive appearance for the senior team.
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Nevertheless, Peterson scored against Brondby and Preston in consecutive preseason friendlies and travelled with the Reds on their preseason tour of America.
He joins a Utrecht side in sixth-place in the Eredivisie, with the club having won two and lost one of its opening three games of the 2014-15 season.