Who captured Mecca and Medina?

Answer 1

I assume you are looking for the answer "Mohammed and the Early Muslims", but Mohammed never declared war on Yethrib (the city which would become Medina). He settled there at the request of the Yethribis to resolve a dispute between two tribes. Mohammed and the Early Muslims did conquer Mecca, though, after difficult battles with Abu Sufyan and other Qoreishi Tribesmen.

In more modern history, both the Ottoman Empire and Saudi Arabia conquered the territory of Hejaz in which Mecca and Medina are located, transferring those cities to those countries in the 1500s and 1920s respectively.

Answer 2

The question comes down to what time period the question is referring to.

Mohammed did conquer Mecca in 630 CE, but he never needed to conquer Medina as they had invited him to be Chief Hakam (Arbitrator) of the city upon his arrival.

The Ottomans conquered Mecca and Medina in 1517, while permitting the local Sharif of Mecca a high degree of autonomy.

In 1803, the first Saudi State conquered Mecca and Medina from the Ottoman Sultanate supported the Sharif of Mecca. In 1813, the Khedivite Kingdom of Egypt defeated the First Saudi State and returned the holy cities to the Ottoman Sultanate.

In 1916, after the Battle of Mecca in World War I, the Sharif of Mecca asserted independence with British assistance and formed the Kingdom of Hejaz. In 1924, the Second Battle of Mecca took place and the Kingdom of Hejaz was overrun by the Second Saudi State (the modern Kingdom of Saudi Arabia).

Saudi Arabia retains control of the two holy cities of Islam and the Kingdom of Hejaz is no more.