Coombs, who is already the club's third signing of the summer after England forward Ellen White and Portuguese defender Matilde Fidalgo, has agreed a two-year deal with City after her contract at Liverpool expired.
"City are a really ambitious club and there are a lot of things in my career I still want to achieve. I feel that being here gives me the best opportunity to do that. I'm really excited to get started," the 28-year-old told CityTV.
Coombs also spoke of her delight to be working with City manager Nick Cushing and is hoping to find new ways to develop her game under his tutelage.
"I've only heard good things from past and present players," she explained.
"I've played with a couple of the girls over the last couple of seasons and they've sang the praises of both Nick and the club, which made my decision easier. He said it would be a great opportunity for me and he thinks I could bring something, and I agree.
“City are a really ambitious Club and there are a lot of things in my career I still want to achieve. I feel that being here gives me the best opportunity to do that."— Manchester City (@ManCity) June 3, 2019
"I think you can always improve technically and tactically. What a lot of people say about Nick is that he finds things you didn't know you could improve on. For me, potentially being a goalscoring midfielder is something I've wanted to aspire to."
Coombs started her career at Arsenal and later spent six years with Chelsea, completing an FA Cup and WSL domestic double in 2015. She has also played abroad, with two separate loans spells in the United States at Los Angeles Strikers.
So far this summer, City have lost star forward Nikita Parris to Lyon and long serving defender Abbie McManus to newly promoted neighbours Manchester United.