The Shell deal, which was first reported by CNBC's Maria Bartiromo, is expected to close in the second quarter of this year.
The acquisition gives the San Antonio-based Tesoro a position in Los Angeles, the only West Coast market where it was not previously represented.
"The refinery fits perfectly with our system, and we expect to quickly integrate the facility into our network," said Tesoro Chairman and Chief Executive Bruce Smith, in a statement.
Meanwhile, the sale will leave Shell with only two wholly-owned U.S. refineries - one in Martinez, Calif., and another in Anacortes, Wash. - on the West Coast. The company jointly owns four other refineries on the U.S. Gulf Coast.
Tesoro Profits More Than Double
Earlier, Tesoro reported fourth-quarter profit more than doubled as stronger refining margins offset maintenance costs at its Washington state refinery.
Net earnings climbed to $158 million, or $2.28 a share, from $69 million, or 97 cents a share, in the year-ago quarter.
Analysts polled by Thomson Financial had expected the company to post earnings of $1.88.
The company said its gross refining margin rose 16%, helped by heavy industry maintenance on the West Coast during the quarter, the company said.
Revenue during the quarter fell to $4.02 billion from $4.36 billion.