The analyst group said online trade within the EU, which was worth £49.1bn, 1% of total business trade, in 2001, would grow as firms transform sales processes and adapt to new trends such as strategic sourcing.
David Metcalfe, an analyst at Forrester, said the UK would be among the countries driving the increase.
"In 2006 Europe's three major markets - the UK, Germany and France - will transact at least 23% of sales online, and their combined trade volumes will represent a whopping 64% of the EU's total online trade," Metcalfe said.
"The rapid growth and high volume of Net-based trade in France, Germany and the UK will pressure proximate countries with deep trading relationships, like Belgium, Austria and Ireland, to accelerate their migration to the Net."
Metcalfe said online trade in industrial sectors, such as industrial machinery, vehicle manufacturing, metals, energy and utilities, will double between 2003 and 2004.
"Growth in Europe's industrial sectors will account for a massive c945bn (£603bn), representing 9.9% of total business trade," he said.
Laggard sectors such as food, textiles and household goods will move online in 2005, while the online trade in the region's £830bn food and beverages sector can be expected to treble between 2004 and 2006, Metcalfe added.