In a statement to the Scottish Parliament committee discussing the The Burrell Collections Lending and Borrowing (Scotland) Bill, Neil McGregor said he endorsed the plan to tour its objects overseas "unreservedly" as it would be "of real public benefit, likely to attract both visitors and works of art to Glasgow."
Tens of thousands of people visit the city's Burrell Collection every year, but the collection's Pollok Park building, in the south side of Glasgow, is in need of a major revamp, believed to cost about £40 million.
The revamp will lead to the building being closed between 2016 and 2020, and the parliamentary Bill is required to alter Sir William's deed of gift so his art treasures can be exhibited abroad while it is closed.
In his statement, Mr McGregor said: "It is sometimes argued that a change to a donor's conditions, even after many decades, will discourage future benefactors.
I believe rather that benefactors would hope future generations would make whatever adjustments were reasonably necessary to maximise the public benefit which they sought to confer."
In his submission, he adds: "The distinction between lending in the UK and lending abroad was perhaps a material one when overseas loans travelled by sea - with the hazards and complexities of loading and unloading at docks.
"It makes no sense today, when loans travel by road and air, in conditions unimaginable 40 years ago."