Mario Balotelli's agent Mino Raiola has revealed that the striker will not be leaving Anfield this summer.
Graham Dorrans has signed a two-year deal with Norwich City following a successful loan spell with the club.
The former Aldershot boss, 52, leaves his role as head of coaching at MK Dons to replace Mickey Lewis, who had been caretaker boss at the Sky Bet League 2 club since Chris Wilder's departure to Northampton in January.
Waddock, who led Aldershot back into the Football League and Wycombe into League 1, officially accepted the job on Saturday morning and will take charge of their Monday night clash at fellow promotions hopefuls Southend.
"I am grateful to Oxford United for having given me this great opportunity, and cannot wait to get started," he told the club's official website. "The club is in a good position, and the immediate priority is to turn that position into promotion at the end of the season.
"In the medium term, the board's vision is to build on the solid platform that has been put together to take Oxford back up the leagues, where a club of this size belongs.
"I applied for this job because I believe that I can be a part of achieving that ambition, and because I fully buy into the board's philosophy of how a football club should be run."
Chairman Ian Lenagan added: "His CV brings the exact mix of attributes we stated we were looking for: success as a manager in the lower leagues, top-class coaching experience, understanding of sports science and a track record of playing attacking football and developing young players through into the first team."