The San Diego Assemblymember and Chair of the California Legislative Black Caucus would be the first Black woman in the position. The nomination is subject to approval in the Legislature.
In a press release, Dr. Weber said, "I am excited to be nominated for this historic appointment as the Secretary of State of California. I thank Governor Newsom for the confidence he's placed in me and his belief that I will stand strong for California. Being the first African American woman in this position will be a monumental responsibility, but I know that I am up for the challenge. Expanding voting rights has been one of the causes of my career and will continue to motivate me as I assume my new constitutional duties."
Weber's nomination comes after the current Secretary of State Alex Padilla was nominated to fill Vice President-elect Kamala Harris's seat in Senate on Tuesday.
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Weber presided over the Electoral College that met in Sacramento earlier this month.
"Dr. Weber has been a champion for civil rights and police reform, authoring a landmark law setting new, higher standards on the use of deadly force by police," the Governor's press release said.
Newsom called Weber, the daughter of sharecroppers, "a tireless advocate and change agent with unimpeachable integrity.'' Padilla called her a fierce advocate for civil rights and voting rights.
The Associated Press contributed to this report.