US lawmakers have 30 days to block the sale, but such action is rare.
BAE beat out F-16 maker Lockheed Martin Corp to win the South Korean competition in 2012.
The first phase of the deal is valued at $200 million, and covers initial design and development efforts, according to the DSCA.
Combined with the second phase, which will upgrade the fighter jets with new avionics and radars, the deal could be worth around $1.1 billion, according to Korean media reports.