Immigrationboards.com

Good afternoon,
I was born in 1960 in London in an American military family. Both parents are American citizens. My dad was serving in London as an American soldier where I was born. I lived in UK until I was 2 years old and moved to USA as an American citizen.
Am I eligible to become an UK citizen and get UK passport? If yes what are my steps? Do I apply in UK Embassy in USA?
Thank you for your help.

My understanding is that anyone born in the UK before 1 Jan 1983 is automatically a British national. This means you should be able to apply for a British passport directly.
https://www.gov.uk/overseas-passports