Mr Vardey said he planned to return to the securities industry from where the Exchange recruited him in 1992. He is to leave next March.
In the spring he was widely tipped as the likeliest internal candidate for the chief executive's job after Michael Lawrence was forced out because of disagreements with the board over the new computerised order book trading system.
But the Exchange board decided not to consider internal candidates, and Gavin Casey was brought in from Merrill Lynch as chief executive in August.
In the stock market, there was no suggestion of anything other than an amicable parting with Mr Casey, in stark contrast to the blazing rows that led to the departure of Mr Lawrence. But Mr Vardey is nevertheless likely to be entitled to a pay-off. According to the annual report all the Exchange's executive directors are on one-year rolling contracts, and he is to leave just over three months after resigning.
The Exchange said: "There are no payments being made to Mr Vardey other than those to which he is contractually entitled under his contract of employment."
Observers believe Mr Vardey is leaving because he helped reorganise himself out of a senior job at the Exchange, which is slimming down and concentrating on its core activities.
This has left less scope for a board which - with Mr Vardey - comprises four full-time executive directors and a chief executive.
The Exchange confirmed that Mr Vardey is not being replaced, and it is expected that his departure will lead to further reorganisation.
Last year he was the Exchange's highest paid executive after Mr Lawrence, earning a salary of pounds 170,000, a performance bonus of pounds 56,000 and benefits of more than pounds 13,000.
Mr Vardey said he had always intended to leave the Stock Exchange after four or five years. He was returning to the securities industry because "that is where I came from, that is the business I know".
Mr Vardey was best known recently for pushing through the new computerised order-driven trading system, which is to be inaugurated next October.
However, the main technical and regulatory elements of the system have now been agreed and by the time Mr Vardey leaves in March it is expected to be in the trial stage.
He was also involved in the Exchange's move from a fortnightly account to rolling settlement and the introduction of the AIM market for small firms.
Mr Vardey's marketing of the Exchange abroad led to a memorandum of understanding with China and the first Chinese share was listed on the Exchange this week.