Flores called on Napolitano to prioritize immigrant student issues, fund academic preparation programs, and review the presidential appointment process.
The announcement last Friday that Napolitano had been nominated for the position caught many university and Washington insiders by surprise.
Napolitano was the unanimous choice of a 10-member search committee that considered more than 300 people for the job.
Napolitano, who attended the private Santa Clara University in California as an undergraduate, has already announced her resignation from President Barack Obama's cabinet.
In the week since she surfaced as the search committee's choice, some faculty members have complained that she is more schooled in politics than higher education.
Several newspapers have taken issue with the secrecy surrounding Napolitano's selection and the short time frame between the announcement and Thursday's vote.
Napolitano will succeed Yudof, 68, who in 2008 became the first president from outside California to lead the UC system in two decades. He had spent 11 years leading the public universities in Minnesota and Texas.
As UC president, Yudof was one of the nation's most highly paid college administrators, earning an annual salary of $591,084 — almost triple what Napolitano makes as Homeland Security secretary — plus car and housing allowances, retirement contributions and other benefits that brought his annual compensation at more than $925,000.
Napolitano will take over at a time of improving but still serious financial challenges for the university system, including rising costs for employee salaries and retirement benefits.
After several years of deep budget cuts, Gov. Jerry Brown earlier this month signed a state budget that boosts funding for UC.
University regents on Wednesday scaled back plans for price increases on graduate programs.
The university had considered raising prices for professional degrees in 29 programs. Instead, regents approved increases for eight programs.