There were no immediate signs of any North Korean retaliation, though it did warn of a "catastrophe" earlier if the exercises were held.
The North considers the waters around Yeonpyeong its territory and has threatened to retaliate for any new drills.
The island was shelled by the North after similar drills last month. Two marines and two civilians were killed.
The U.N. Security Council scheduled an emergency closed-door meeting Saturday about the escalating tension on the Korean peninsula.
After meeting for hours, the Security Council failed to agree on a statement regarding the rising tensions.
Russia called for the meeting and said the Security Council must send "a restraining signal" to North Korea and South Korea and help launch diplomatic actions to resolve the tension.
China reportedly objected to condemning North Korea.
South Korea said the drills were routine, defensive in nature and should not be considered threatening.
Residents of the island were evacuated to the mainland before the drills began.
The Associated Press contributed to this report.