Wilson was absent from the squad that left Glasgow on Tuesday for Rangers' pre-season tour in Australia, which was attributed to a hamstring problem.
The 18-year-old centre-back turned down an offer to remain at Ibrox.
A product of Rangers' Murray Park youth project, Wilson had only 12 months of his Ibrox contract remaining.
Danny was entering the final year of his contract with the club and had indicated that he felt it was in his interests to move on
Rangers chief executive Martin Bain
Had the player allowed his current deal to expire, Rangers would have expected to receive only £500,000 in compensation.
"Danny was entering the final year of his contract with the club and had indicated that he felt it was in his interests to move on," Bain told the Rangers website.
"Given that and the value of the offer from Liverpool it was deemed appropriate to accept that offer given the player wanted to go."
Rangers had been hopeful that Wilson would sign a contract offered to the player in April.
He is tall and a natural born leader and would fit finely into our squad
Irrational Explanation
The day after he scored his first goal for Rangers, in a 4-1 win over Hearts on 27 March, manager Walter Smith said he expected Wilson to follow the example of fellow Rangers teenager John Fleck by signing a contract extension.
However, that did not come to fruition and Bain admitted that the two sides had yet to reach agreement and that Liverpool had made an enquiry.
Wilson became a first-team regular at Ibrox last season and made 24 appearances for the Scottish Premier League champions.
Source: BBC Sport
