Graeme Lee’s side will host Johnnie Jackson’s Addicks later this month after the draw for the last eight took place on Thursday morning live on talkSPORT on the Jim White and Simon Jordan show.
The match will take place at the Suit Direct Stadium the week commencing January 24.
Pools booked their spot in the quarter finals with another impressive display against League One opposition on Tuesday when they edged past Bolton Wanderers.
Matty Daly’s goal six minutes from time was enough to settle the tie and move Lee’s side to within two wins from a Wembley final in April.
Daly’s strike was his fifth of the competition and it marked the second successive tie in which Pools have toppled League One opposition having comfortably beaten Sheffield Wednesday at Hillsborough in round two.
Pools finished second in their group behind Carlisle United but remained unbeaten with one win and two draws.
Speaking after the win over Bolton, Lee shared the excitement among his squad ahead of the quarter final draw.
"We’ve got an unbelievable chance. Everyone is questioning when the draw is. It’s exciting and we will be looking at the draw and looking at the next challenge,” he said.
Elsewhere in the draw Rotherham United will host either Exeter City, Portsmouth or Cambridge United, Sutton United will face Harrogate Town while either Arsenal U21’s or Chelsea U21’s will host Wigan Athletic.
Pools continue in cup action this weekend when they host Blackpool at the Suit Direct Stadium in the third round of the FA Cup.