The 18-year-old defender passed a medical on Wednesday afternoon after the Reds and Rangers agreed a deal worth up to £5million.
Wilson came through the youthranks at the Ibrox club, signing his first professional contractthere three years ago.
After a promising debut season last term, Wilson was awarded both the ScottishFWA Young Player of the Year award and the Scottish PFA Young Player ofthe Year award.
Danny boy: Wilson (right) leaves Liverpool's training ground on Wednesday
'It's a great feeling to sign for Liverpool. Wherever you goeveryone knows Liverpool FC and I am just very happy to be here,'Wilson told the club's official website.
'This is a massive challenge for me. This is one of the best leaguesin the world and I will be playing for one of the biggest teams in theworld.
'Coming here from Scotland, people may say I might not be ready forthis, but that is a challenge I want to put on myself and that's thereason I came here.
'Everyone knows about the history of this football club with 18 league titles.
'It wasn't a difficult decision to come here as Liverpool are not ateam who come in for you every day, so I can't wait to get started.
'There were other clubs interested in me who are in the ChampionsLeague, but once Liverpool came in for me there was only one team Iwanted to go to.'
Liverpool had been tracking Wilson for several months and the teenager was pulled out of theRangers squad that set off on a pre-season tour of Australia.
Rangers will receive £2m up front with add-onslinked to games played, taking the total value of the deal to £5m.
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