The southpaw English batsman smashed his ton in 157 deliveries and hit 15 boundaries. Cook is 13th batsman to have equalled Bradman's record.
The England opener took 131 matches to reach this milestone while Don Bradman achieved this milestone in 52 matches.
Winning the toss, Cook decided to bat in the second Test match against Pakistan.
Earlier on May 31, Cook became the youngest batsman to complete 10,000 Test runs.
The England opener broke Master Blaster Sachin Tendulkar's record, which India's cricketing legend held for more than a decade.
He also became first English cricketer to score 10,000 runs in Test cricket. Sachin was 31 years and 10-months-old when he achieved this landmark against Pakistan in Kolkata in March 2005.