Hearts' ongoing administration means new players cannot be signed, but Wilson was registered at Tynecastle when he arrived on an initial loan deal from Liverpool in January.
The defender's contract at Anfield has now expired, and a statement on the Hearts website confirmed a permanent deal has gone through.
The statement read: "As the 21-year-old is already registered with the club there is no restriction on his move."
Wilson has joined three senior players in agreeing to a pay cut, and manager Gary Locke said: "I am really pleased.
"Danny was already due to be part of the team and the administration has made no difference to his status.
"I appreciate that there have been some difficult decisions made regarding player redundancies.
"But given that Danny has agreed to a wage cut and is happy to be playing for Hearts, this gives us an opportunity to improve the team for the forthcoming season so why wouldn't we jump at the chance to have him on our side?"