It says the recent high profile failures of dot.com companies will have little effect as the technology is embraced increasingly vigorously by long established businesses.
It says that most businesses now had to "stop worrying about being Amazoned and start worrying about being Schwabed".
In other words, the threat to companies is now coming from established rivals utilising new technology - as Charles Schwab did in the stockbroking world - rather than start up dot.coms, like online bookseller Amazon.
"Media discussion of the internet can sometimes appear to be focussed on the fortunes of the dot.com companies," says Gartner's report.
It is convinced that this is a misleading picture of the real internet economy, with so-called bricks-and-clicks companies able to find savings and set up profitable online operations more quickly.
The report found a wide variation across Europe in the speed and take-up by consumers and businesses of internet services - whether via PC, TV or mobile phones.
Netherlands lead, France lags
It estimates that the value of e-commerce sales in Germany will rise from $12.6bn this year to $317bn by 2,004. The UK also sees rapid growth, from $11.8bn to $235.5bn.
France, which this year lags behind with $2.7bn, will rise to $121.7bn - but still remain only slightly more than half the UK's market.
But the Netherlands, followed by Sweden and Switzerland would have the highest rate of e-commerce transactions, when expressed as a percentage of their overall economy.
In other regions, Gartner's research puts the United Arab Emirates and Lebanon at the forefront of Middle East internet usage.
Regional variations
In Eastern Europe the Czech Republic is followed by Hungary at the head of the table, with Ukraine and Bulgaria at the bottom end of e-business adoption.
Within Europe, it identifies three separate groups.
The first is the UK, Netherlands and Scandinavia, where business sees the internet primarily as a means of boosting productivity.
Businesses in the Central Europe countries, including Germany, France and Switzerland, are more interested in reducing costs - while businesses in the Mediterranean countries have much greater interest in increasing their revenues.
Dick Gillespie, Cisco Systems' UK chief, believes the internet economy's growth will allow faster growth without inflation across Europe as productivity increases.
Venture capitalists
As to the bursting of the dot.com bubble earlier this year, he said that many of those companies had floated on the stock market much earlier than in the past.
This meant that investors who bought shares were getting involved at a start-up stage normally the sole preserve of venture capitalists.
This meant, said Mr Gillespie, that investors should expect about the same strike rate as venture capitalists operate on - from 10 investments expect five flops and hope for three winners.
But the publicity gained by failures such as Boo, Boxman and Clickmango had diverted attention from the huge investments in new technology being made by long established organisations.
This would more that outstrip the negative effect of what Gartner expects to be a 90% failure rate for dot.coms.
But whichever way one looks at the internet economy, this latest piece of research suggests that even the most internet savvy European countries will remain a fair way short of the US.