Watt joined the AFP, which has more than 30,000 members, in 2006 as vice president of international development before becoming chief programmes officer in October 2007.
He worked for nearly 10 years at the IoF as head of policy and ultimately deputy chief executive before joining the AFP.
He takes over from Paulette Maehara, who is retiring after almost 13 years with the organisation, and will take up his new role on 23 March
Lindsay Boswell, former chief executive of the Institute of Fundraising, said it was a commendably "non-parochial" appointment for the AFP to make. Watt now had the world's most influential fundraising job.
A statement from the AFP said it had selected Watt after an extensive international search. "We believe he is clearly the best choice to lead the AFP at this important time for our profession," it said.
Watt said he was honoured to be offered the role. "I am committed to making the AFP an increasingly authoritative voice on philanthropy around the world," he said.
"One of my most important goals will be to maximise AFP’s many partnerships and assets to make it a vital leader within the philanthropic community."