Brown had long been seen as the natural successor to Tony Blair, the current prime minister, who last week announced that he would stand down on June 27.
Conceding defeat, McDonnell said Brown's overwhelming victory meant that ordinary party members would have no say in chosing Labour's next leader.
"Naturally, I congratulate Gordon and wish him every success in government, but it is a great shame that Labour Party members will now not be allowed a vote on the leader of their party or the party's future direction," he said in a statement.
Brown will lay out his policies at 10 campaign-style "hustings" around Britain over the next few weeks followed by a major speech at a Labour party conference on June 24.
A deputy leadership contest is being held in parallel, after John Prescott, the incumbent, announced that he would step down at the same time as Blair.
Five of the six candidates have already secured more than the 45 nominations while Hilary Benn, the international development secretary, is only three nominations short.
Results for both leadership contests are due to be formally announced at a conference on June 24.