The 26-year-old right-back, who arrives at The Valley from Elland Road on a free transfer, becomes the Addicks' second signing of the summer after Spanish central defender Miguel Angel Llera.
Parkinson said: "I'm delighted to get Frazer on board. He's exactly the type of character we're looking for.
"He's a good player and he's got lots of experience in this division and higher. He's been at Leeds a long time and perhaps now's the time for him to have a fresh challenge.
"He will be a great addition for us and we look forward to working with him."