Walker, who moved to Sixways from the Ospreys last year, will be released early from his contract and head north this summer.
The 31-year-old has made 13 appearances for Worcester and scored four tries.
"Nikki retains strong international aspirations and has been a part of the Scotland set-up during the recent Six Nations campaign," Worcester head coach Richard Hill said.
"His move to Edinburgh should help his ambitions to play for his country once again, and he will leave us at the end of the season with our best wishes."
Walker added: "I have enjoyed my time in Worcester, but an opportunity has arisen for my family and I to return home to Scotland. This opportunity was too big for us to turn down."