The Scottish Premier League side were recently put under a transfer embargo with the condition that they would have to let go of one player in order to bring in another.
Wilson, 22, will remain at Tynecastle Stadium until the end of the season.
"Danny is a quality player and someone we know a lot about," manager John McGlynn told the club's official website.
"Even at such a young age, he brings a lot of experience and not only will he be a very good addition to our squad, he will be a good influence on the young players we have here."
Wilson started his professional career with Rangers in 2008 before a move to Anfield two years later.
However, the versatile defender has failed to make an impact on Merseyside.