Cox also named a new head of the SEC's San Francisco office.
Tyson, 60, said she would emphasize "swift and vigorous enforcement of the securities laws" and seek to "reinforce our cooperative working relationships with our fellow regulators at the federal, state and local levels."
A Stanford Law School graduate and a career SEC lawyer, Tyson joined the L.A. office in 1982 in its enforcement unit. Since 1993 she has headed the examinations unit, which inspects brokerages, investment advisors and mutual funds.
In San Francisco the regional-director job went to Marc Fagel, 41, who has been co-acting chief since October.
Fagel, who got his law degree from the University of Chicago Law School in 1991, joined the SEC's San Francisco office in 1997. He has been regional enforcement chief since 2005.
Randall Lee headed the SEC's L.A. office from 2001 to last July. He has since opened an L.A. office for Washington law firm WilmerHale. Helane Morrison was San Francisco office chief from 1999 until October, when she departed to become general counsel at Hall Capital Partners, a $22-billion-asset investment management firm in San Francisco.
Although the next occupant of the White House is likely to name someone to replace Cox as SEC chairman, Tyson and Fagel will probably remain in their jobs. That's because SEC chairmen historically haven't summarily replaced the agency's regional chiefs.
The L.A. office's territory is Southern California, Arizona, Nevada and Hawaii. San Francisco covers Northern California and the Pacific Northwest.