The Imams are most probably selected by the Genereal Presidency or by the Imams of the Haramain themselves. Then the Recommendation is sent to the Custodian of the Two Holy Mosques i.e the King of Saudi Arabia Salman bin Abdulaziz Al Saud. Its then up to the King to approve or not.
The King Approved the Appointment of two Imams this year. Sheikh Salaah Ba Uthman, to lead in Masjid Al Haram,who imitates the Late Sheikh Ali Jabir who was the Imam of Masjid Al Haram and Sheikh Muhammad Khaleel Al Qari was appointed to lead Taraweeh in Masjid Al Nabawi.
Sheikh Muahammad Khaleel Al Qari belongs from Muzaffarabad, Azad Kashmir region of Pakistan. His father migrated to Madinah, Saudi Arabia in 1960s and became a renowned Qari and Teacher. He was also the Teacher of Sheikh Muhammad Ayub (RahimuAllah) and Sheikh Ali Jaber (RahimuAllah).
Sheikh Muhammad Khaleel Al Qari reportedly also led Salah in Masjid Quba in Madinah.
Inside the Haramain is a subsidiary of ‘Haramain Sharifain’, the second largest Harmain Source on Digital Media.