Stephenson, who operates at either full-back or wing-back, has agreed a four-year contract to move to Bolton, who are preparing for their first season back in the Championship for seven years.
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The 22-year-old did not make a single first-team appearance for the Reds and spent the past two seasons on loan with Dundee United in the Scottish Premiership.
"It's brilliant being a Liverpool player and they've given me a lot and taught me a lot, but there's nothing like playing men's football," he told Bolton's website.
"You can't replicate that at Liverpool playing for the 21s. I found that I wasn't going to get the chance to play for the first team every week and that's why I made the decision to come here."