The 34-year-old defender succeeds Bruno Guimaraes, who left the club for Arsenal earlier this month after captaining the Magpies for two seasons.
Burn’s appointment comes during a period of change at St James’ Park, with the club turning to his experience and leadership to guide the squad.
The defender is Newcastle’s fourth-highest appearance maker among the current squad and has earned 11 England caps, including three at this summer’s FIFA World Cup.
His vocal presence, defensive experience and strong connection with supporters were key factors behind the decision.
"He puts the interests of the team ahead of his own every time he steps onto the pitch and always gives maximum commitment in everything he does,” said head coach Matthias Jaissle.
“Off the pitch, he leads by example in how he conducts himself. Not many people understand what this club means to the city better than Dan and that experience will be vital in helping guide our younger players through this period of change and adaptation.”