As part of the deal, Derby left back Jay McEveley has moved to SE7 also on a three-month loan deal.
McEveley, 23, has experience of the Premiership and Championship with the Rams and Blackburn Rovers and can also play at centre-back.
The replacement for Varney is Sheffield Wednesday's Deon Burton, who moves to the Addicks on a three-month loan with a view to a permanent free transfer in the new year.
Caretaker boss Parkinson said, "There's no fee involved for Deon and he's a player I've admired for a long time. What concerned me slightly is that if Andy Gray got injured, we lacked a hold-up player and I was struggling to find two strikers who complemented each other.
"But with Deon here, it gives me the option to replace Andy and they also have the ability to play together. All over the football pitch you need partnerships, and it's important you get the right balance in all areas.
"I'm also delighted to bring Jay in. Despite his young age, he has got a lot of experience, both in the Premier League and the Championship. He's a big, strong, athletic full-back, who will give us much-needed consistency in that area.
Charlton now have seven players on loan and can only put five loanees in a matchday squad of 16 and Parkinson knows that he'll have to make a big decision in which of those players will start Saturday's relegation battle with Southampton.
"We're aware that we can only include five players in the 16 so it's up to myself, Mark Kinsella and Phil Chapple to balance that out.
"But I felt it was very important that we changed the dynamics of this group around, and I feel that's what we've done."