Brighton's clash with Palace on Monday, January 8 has also been selected for the VAR trial, with the technology employed in selected fixtures throughout the rest of the competition.
"The FA has always been open to trialling new innovations and was heavily involved in the advancement of goal-line technology before it was introduced," said the FA's director of professional game relations Andy Ambler.
"The trialling of the VAR system in this season's Emirates FA Cup from the third round is a continuation of that and further demonstrates that whilst being the most famous and historic domestic cup competition in the world it is also modern, progressive and innovative."
It is one of three FA Cup matches to be screened on BT Sport across the first weekend of the New Year. Chelsea's trip to Norwich on Saturday, January 6 and Arsenal's visit to the City Ground the following day will also be shown.
Meanwhile, Gary Lineker will host the BBC's coverage of the Merseyside derby on Friday, January 5. The match between Liverpool and Everton at Anfield will kick-start third-round weekend, but has reportedly been considered 'too high profile' for a VAR trial.
Lineker will also be in the studio for West Ham's trip to Shrewsbury, while Dan Walker will present coverage of Chelsea's visit to Norwich.
FA Cup third round
Friday, January 5
Liverpool vs Everton
Saturday, January 6
Norwich vs Chelsea
Sunday, January 7
Newport vs Leeds
BBC One Wales
Shrewsbury vs West Ham
Nottingham Forest vs Arsenal
Monday, January 8
Brighton vs Crystal Palace