International Business Times published on 4 February 2016 an article titled "With China's Naval Base, Djibouti Could Become 'Africa's Singapore'" by Morgan Winsor. The article says China and Djibouti have signed a 10-year lease for the base at Obock, with China paying $100 million per year in rent. The article adds that "the facility will house some 10,000 Chinese troops."
The article does not provide the source of the information concerning the details of the agreement. The number of 10,000 Chinese troops sounds wildly high. Certainly, China does not need 10,000 troops to support its 3 ships that operate in the anti-piracy operation in the Gulf of Aden and this is ostensibly the reason for the support facility. I would take this figure with a grain of salt.