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The former Man Utd trainee has made just two appearences this season and has now joined Mark Cooper's FA Cup heroes in a bid to gain regular first-team football.
Should he impress the Tamworth boss, it is expected that Williams will sign a deal to keep him at the Lamb Ground until the end of the season.
The skillful striker - who has also played frequently in midfield - has scored just once for the Magpies since joining in March 2004 under then-manager Gary Mills, that goal coming in a 2-1 victory over Cambridge Utd last term.
The diminutive player, though, has often been unable to adapt to the Magpies increasingly direct style of play, with Williams' best work coming when the ball is played on the floor.
The talented marksman now becomes the fourth of Mills' signings that Thordarson has moved-on during the transfer window, following Glynn Hurst, Matthew Gill and Tony Scully through the exit door.
He leaves with the best wishes of all at NCM.