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As part of the change, Thunder have applied to Newcastle City Council to make Kingston Park their home ground.
The switch comes after Newcastle Rugby Limited, owned by Falcons rugby union chairman Semor Kurdi took over the rugby league side in May.
"It was a commonsense step," managing director Keith Christie told BBC Sport.
"We're keen to make sure we don't forget our birthplace in Gateshead, but we have to ensure we move forward and unfortunately that means changing the name."
Thunder play in Championship League One - two steps below the top-flight. The side previously played in the Super League as Gateshead in 1999.
Christie said one of the club's priorities would now be to build up the fan base.
"We always want fans to come and it's a business decision we've taken to move here," he added.
The Rugby Football League has approved the name change.
Gateshead Thunder have rebranded as Newcastle Thunder, returning professional rugby league to the city for the first time since 1938.