In a statement released this morning, the company said he would be replaced with immediate effect by Erik Engstrom, currently chief executive of Elsevier, who joined the company in 2004.
Reed Elsevier chairman Anthony Habgood said Smith had the "difficult task of leading Reed Elsevier during unprecedentedly turbulent economic times".
Erik Engstrom, who will be paid an annual salary of £1m and could earn three and a half times that figure in bonuses and incentives, said the business is "strongly positioned in attractive markets" and that he was confident "we have the resources and ambition to be highly competitive".
The company, which earlier this year reported revenues for 2008 of £5,334m, also released a trading update this morning in which it said ad revenue was being hit by the global recession but its restructuring programme was "on track to deliver the targeted cost savings".
It added: "The major professional markets, accounting for the majority of Reed Elsevier's business, are proving more resilient than most but not immune from late cycle pressures given the subscription nature of much of the revenue."
The company said Reed Business Information (RBI), which houses its magazines division, "continues to face difficult trading conditions particularly in advertising markets" and it continues to take substantial costs out of the business.
"The divestment of controlled circulation magazines in the US and certain other print titles is in progress to reposition the portfolio with further development focused on online data and lead generation services."
In July, RBI reported a 37% slump in operating profit in the six months to 30 June. The division, which Reed abandoned plans to sell in December 2008, reported revenue of £463m in the period, a fall of 4% year on year.