The player and clubs have reached agreement and City are now awaiting international clearance, writes Alan Campbell.
The 26-year-old midfielder will make history by becoming the first fully professional player in Scottish women's club football. Her arrival will strengthen City's bid to reach the quarter finals of the Uefa Women's Champions League for the first time.
"The chance to sign a player of her quality doesn't come along often," said Laura Montgomery, City's general manager. "To take the club forward on the European stage you need world-class players and, in our opinion, Jess is in that category."
Fishlock, who has scored 22 goals from midfield for Wales in 67 games, is on a full-time contract with Seattle, whose inaugural season in the Women's National Soccer League ended on Saturday.
She started her career with Cardiff City Ladies before moving to Bristol Academy, where she was English Womens Super League players' player of the year in 2012. She has also played for AZ Alkmaar, with whom she won two Dutch titles, and Melbourne Victory in Australia.