Wood is the second signing of the month.
Chris Wood is from New Zealand.
The 30-year-old, who joins for an undisclosed fee, has agreed a contract until the end of the 2023-24 season.
Eddie Howe targeted attacking reinforcements after it was learned that Callum Wilson would be out for eight weeks with a calf injury.
Wood is the second signing of the month.
The player's release clause in his contract was triggered by the fact that he was to be sold to a rival.
Wood said that he was delighted to be a player for the club.
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.
I can't wait to get on the pitch and repay the faith they have in me, especially with a vital part of the season ahead of us.
The Football News Show asked how much Wood will be missed.
Wood is a great fit for the team.
Wood scored 53 goals in 165 games for the Clarets, including three in 17 league appearances this season.
Sean Dyche has a major problem after losing one of his most experienced forwards.
The two teams are both on 11 points in 18th and 19th place in the top flight, with two games in hand.
"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," said Howe.
He is a very dangerous attacking threat, has a lot of experience in the premier league, and I really like him. He will be a good fit for us.