The amendment to Law 21.3 follows last year's row at the Oval when Pakistan lost to England by forfeit for refusing to take the field after being accused of ball tampering.
The rule change was adopted at a two-day ICC board meeting, which ended in Cape Town on Friday. It takes immediate effect.
"The Board's decision reflects the fact that the match referee is the chief executive of the match, the person who has overall responsibility for the way the game is played and officiated," ICC chief executive officer Malcolm Speed said in a statement.
"This decision does not, however, detract from the on-field role of the umpires and they would, of course, still remain an integral part of the process of awarding a match in those circumstances."
The ICC said umpires would still have responsibility for determining the end of a match in all other circumstances.
The decision to amend the law relating to teams refusing to play was a direct response to last year's chaotic end to the Test match between Pakistan and England.
Pakistan refused to continue playing after the two umpires, Australia's Darrell Hair and West Indian Billy Doctrove, penalised the team five runs for ball tampering, a charge they hotly disputed.
Under the existing laws, the umpires had no alternative but to award victory to England, though the repercussions did not end there.
Pakistan captain Inzamam-ul Haq was later banned for four one-day games for bringing the game into disrepute. He was cleared of ball tampering.
Hair, who was blamed by Pakistan for causing the row, was later sacked from the ICC's elite panel of umpires.