The left-handed opener is also the 12th batsman to reach the landmark.
Cook joins Sachin Tendulkar, Rahul Dravid, Sunil Gavaskar, Ricky Ponting, Steve Waugh, Allan Border, Kumar Sangakkara, Mahela Jayawardene, Brian Lara, Shivnarine Chanderpaul and Jacques Kallis on the list.
The 31-year-old reached the milestone as England started the task of scoring 79 runs in the second innings to win the test and take an unbeatable 2-0 lead in the series.
