The Italian government had hoped to appeal the ruling - which was made by the court earlier this year - by taking the case to the ECHR's Grand Chamber, but a spokesperson for the court said on Thursday that the request had been rejected.
"Five judges from the Grand Chamber have decided to reject this request, (so) the judgement of March 4 is therefore final," the spokesperson for the Strasbourg court said.
The case relates to an insider trading case which was investigated by the regulator of the Italian stock exchange, Consob.
The watchdog censured the lawyer of the Agnelli group, Franzo Grande Stevens, for misleading the markets by concealing talks that the company was holding over a financial operation involving the car manufacturer Fiat.
As well as the sanctions imposed by the watchdog, criminal proceedings were also launched against Grande Stevens, and against two companies involved, Agnelli and Exor.
But judges at the ECHR decided unanimously that Italy had violated the right not to be tried or punished twice for the same offence.
The European court decided that "although the sanction was described as 'administrative' in Italian law, the severity of the fines imposed on the applicants meant that they were criminal in nature."
It also ruled that the criminal charges were based on "identical facts" to those in the earlier case, for which those involved had already been sentenced.
As a result, the court called on the Italian authorities to close the criminal proceedings "as rapidly as possible".
The case could set a precedent in Italy, which may now have to change its legislation on the subject in order to avoid further cases being brought to the ECHR.
In France, the case has been closely watched by the financial services authority (AMF), which monitors the stock exchange, since the system in that country also means that people can be tried twice both by the AMF and in the criminal courts for the same offence.
Charlotte Plantin, a Paris-based lawyer at Solferino Associates who is currently working on an insider trading case involving the aluminium firm Pechiney, said that French law would have to change to comply with the European ruling, or the country would "inevitably follow Italy in being convicted in similar cases".