The New Zealand international has signed a two-and-a-half-year contract at Saint James’ Park.
Wood is Newcastle’s second signing of the January transfer window following the arrival of Kieran Trippier from Atletico Madrid.
The 30-year-old spent four-and-a-half years at Burnley, having joined from Leeds United in the summer of 2017, and made 165 appearances for the Clarets, scoring 53 goals.
Newcastle moved swiftly to activate Wood’s release clause after losing top scorer Callum Wilson to injury for the next two months.
"I have played at St. James' Park a few times and it's an amazing place, so to have the chance to represent this club with those incredible supporters behind me and my team-mates is very special," Wood told the club website.
"The club and manager have been first class during this process, and I really can't wait to get onto the pitch and repay the faith they have in me, especially with a vital part of the season ahead of us."
Newcastle manager Eddie Howe added: "Chris is an important signing for us at a crucial time and I'm very pleased we have been able to move quickly and bring him here.
"He is a very dangerous attacking threat, has a physicality and character that I really like, and he has vast experience in the Premier League. He will be a great fit for us."
Wood could make his debut for 19th placed Newcastle against Watford this weekend.
