The 21-year-old has been on the books at Liverpool since 2005, coming through the academy but going on to make just one senior appearance for the Reds so far.
"[Klopp] is very easy to speak to. I had a few conversations with him, I let him know I wanted senior football and then he told me his view of it," Wilson is quoted as saying by BBC Sport.
"I was able to get out at the end of the window and I'm delighted to be at Hull. But I have been at Liverpool since the age of eight, so that's always been my dream to play in the first team. Hopefully I can do that, if not next season then in the future sometime."
Wilson has scored three goals in seven appearances for Hull this season.