Peaches Golding will become the first black woman to be the Queen's representative in the UK this weekend.
Her father, Charles Hauser, won a legal battle in 1947 after he refused to move to the back of a bus in North Carolina.
She said the "fabulous" role would help her "level the playing field for Bristolians".
"My father sat at the front of a bus and, at the time, the people on the bus believed he had to sit at the back because he was black," she said.
"Actually, it turned very ugly but my father was able to get legal assistance and brought a case against the bus company."
Ms Golding, Bristol's High Sheriff in 2010, said watching her father question injustice continued to inspire her, and guided what she wants to achieve.
"The things that makes my heart beat faster are about creating a fairer and just society. So how do we reduce some of our problems around homelessness, around people coming out of prisons?
"This gives me another opportunity to see how we can level up the playing field for Bristolians."
Bristol did not get a lord lieutenant until 1996, although the role has existed elsewhere in the country since the 1540s.
It is largely symbolic, focussing on promoting civic, voluntary and business activities.
The role has never been held by a black woman before and Ms Golding - who settled in Bristol with her husband in 1992 after working in Nigeria - will remain in post for the next 12 years.
"Somebody had to be first," she said.
"Nationally there's a lot of interest in it, but I'm delighted the Queen has appointed me to the role. For me that's the important thing."
The daughter of a US civil rights campaigner says her father's fight for justice will inspire her as the new Lord Lieutenant of Bristol.