A fee was agreed on Sunday before the negotiation of personal terms and a medical on Monday morning.
The 25-year-old joins Liverpool late on deadline day as the Premier League champions look to mitigate the impact of a defensive injury crisis.
Virgil van Dijk, Joe Gomez and Joel Matip are all out injured, forcing the likes of Fabinho, Jordan Henderson, Nathaniel Phillips and Rhys Williams to fill in at centre-back.
“I’m obviously delighted to be here," Davies said. “It’s a huge opportunity. Obviously it came as a bit of a surprise when it first came but once you start to get your head around it, the opportunity that is in front of me is incredible. I’d be silly to not make the most of it and learn off the players [at the club].
“I’ve never actually been to Anfield and I haven’t had a look around yet. I had a quick look out and had a look at the pitch and it looks like carpet, which obviously you’d expect.
“I haven’t actually walked out of the tunnel yet, so I’m looking forward to that. Just to be in this kind of atmosphere is brilliant.”
Davies' age and affordability appealed to Liverpool, as did his recovery pace, a key attribute given the high line played by Jurgen Klopp's team.
The new signing will be available to make his debut in Liverpool's Premier League game against Brighton on Wednesday night.
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