The resignation follows fellow Shadow Cabinet member Hilary Benn's sacking last night and Britain's vote in favour of Brexit. Alexander wrote:
It is with a heavy heart that I am writing to you to resign from the shadow cabinet.
The result of the referendum last week means that our country is facing unprecedented challenges.
Those who will be hit hardest by the economic shock associated with the vote to leave the EU need a strong opposition, as do those communities who fear rising levels of intolerance, hatred and division.
More than ever, our country needs an effective opposition which can hold the government to account and which is a capable of developing a credible and inspiring alternative to an increasingly rightwing and backward-looking Conservative party.
As much as I respect you as a man of principle, I do not believe you have the capacity to shape the answers our country is demanding and I believe that if we are to form the next government, a change of leadership is essential.
I would like to thank you for the opportunity to serve in the shadow cabinet.
Alexander did a solid job during her brief tenure and Corbyn is the most incompetent party leader since IDS - quickly proving himself to be insular, egocentric and fundamentally thick.
It's unfair to blame Corbyn for Brexit, as a large minority of Labour voters would have voted to leave in any circumstances and his "seven and a half out of ten" position on the EU was a fairly accurate reflection of Labour voters' sentiment. But now is a time for leadership and Corbyn is no leader.
And if you needed any further evidence of the necessity of Alexander's decision, rumours are now swirling that Diane Abbott is to be Corbyn's new Shadow Foreign Secretary.
Whoever's in charge, it is hard to see how Labour reconciles its Europhile, cosmopolitan wing with its Europhobe vote in its historic northern heartlands. It's easier to imagine Labour becoming reduced to a London-only party than it is to see a unifying figure emerging from another leadership election.