Mahmood, 55, currently Pakistan's ambassador in Turkey, was granted a visa by India on Friday, the sources said.
He may take up his new assignment either at the end of this month or early next month, they said.
Mahmood will replace Abdul Basit who has already completed his three-year tenure in New Delhi.
Basit is likely to be appointed as head of Foreign Service Academy in Islamabad.
Mahmood is a career diplomat, who joined the Foreign Service of Pakistan in 1985.
His first posting abroad was in Pakistan Embassy Ankara where he served from 1991-1994. He is one of the senior most officers of the Pakistan Foreign Service, who knows Turkish.
He has wide experience in the diplomatic service having served in various Pakistan missions abroad including Washington, New York, Ankara.
Mahmood served as the Ambassador of Pakistan to Thailand from 2009-2013.
He holds masters degrees in History and International Relations.
Basit had earlier threatened to resign after he was overlooked and his junior Tehmina Janjua was appointed as Foreign Secretary but the situation has cooled down.
Initially, it was expected that Basit might go on a long leave after he was called back from New Delhi but now he is expected to join as chief of FSA.