The 22-year-old has been with the Cherries since 2013, but has struggled to force his way into the first team having enjoyed loan spells with six clubs, including Leyton Orient, Yeovil and Gillingham.
As a result, Cornick has opted to depart the club in search of first-team football and has signed a two-year deal with Nathan Jones' men to become their ninth signing of the summer.
"I've been an admirer of Harry's for many years now," Jones told his club's website.
"We tried to get him last year but it wasn't possible, so when we knew he was available this time, we went straight into him.
"Fair play to the board, they've backed me once again on another signing which will provide extra competition in the attacking area.
"He's different to what we've got. He can play wide, but we see him as a real quick front man who is a good age.
"He's brave, and he's shown that with the loans he's gone on. He is committed to playing football games. He's not prepared just to stay in the comfort zone at Bournemouth.
"He had a number of offers, but chose to come here so we are delighted and are looking forward to working with him."