"We obviously played the test up there (in June) and it was nice to spend some time there. I quite enjoyed the city and am looking forward to going up."
Yorkshire's head coach, former Australian fast bowler Jason Gillespie, says Williamson was top of the list of contenders they considered to join the county.
"Once we knew that Gary was unavailable, because of his international call-up, we made a conscious effort to bring in a proven international batsman to help bolster the squad," said Gillespie.
"The decision was made in consultation with Martyn Moxon, Andrew Gale, and Michael Vaughan, representing the board on cricketing matters, who all played a pivotal role in bringing in Kane. It is the right thing to do."