The 22-year-old has penned a one-year deal with Preston after joining on trial at the start of preseason.
Speaking to iFollow after signing, Ben said: "I'm very excited for the deal to be done. Obviously I've been on trial for a week now and things have gone pretty well, so I'm buzzing to get started as a Preston player.
"Obviously when I got called and told I could come and train I was buzzing. I wanted to show the gaffer what I could do, luckily I've earned a contract out of it.
"He's tried to get me at his older clubs a few times and unfortunately things haven't worked out there, but now we can work together and I'm a fan of how he plays football, so I'm really excited to get going."
Woodburn ended a 16-year-stay at Liverpool when his contract expired at the end of last season.
He became the club's youngest ever goalscorer when he netted against Leeds in the EFL Cup in 2016 aged 17 years and 45 days.