The 29-year-old Afghanistan-born forward will join City in January, after finishing the season with her current club, Portland Thorns, in the United States.
Nadim was part of the Danish squad who were beaten in the final of Euro 2017 by hosts Netherlands.
"I always wanted to come back to Europe to play for a big team," she said.
"I'm honoured to join Man City because it's one of the biggest clubs in Europe. Being a part of that and contributing to the goals they have is a dream come true."