The 21-year-old has been linked with a loan move to both sides of the Old Firm this summer.
Wilson is currently part of Jurgen Klopp’s pre-season squad as the Liverpool manager takes a closer look at the player, who scored a brace in the club’s first friendly.
““I’m delighted to sign the new deal,” he told Liverpool’s official website. “When it got offered to me, I was desperate to get everything sorted so I could sign it fairly early on in pre-season because I want to focus on playing football.
“So, now this is sorted, I feel I can do that and push on and try and impress.”
A Wales international, the forward spent time on loan at Hull City last season in the Championship, scoring seven goals in 13 games.
It was form which attracted Rangers and Celtic bosses Steven Gerrard and Brendan Rodgers who will know the player through their connection with Liverpool.
It was reported that if Liverpool were to allow the player to go out on loan again it would be to the Championship with Liverpool reluctant for Wilson to move to Scotland.
He said: “I think my short-term focus is to keep trying to impress the manager day in, day out in training and, the minutes I get in pre-season, try and impress.
“[I want to] keep trying to score goals, [get] assists, help the team out and then I’m not looking too far beyond that.
“I feel if I do well enough here, everything else will take care of itself.”