Another six people accused of involvement in the violence were acquitted.
Those convicted received jail terms averaging nearly three years but, in line with standard judicial procedure in Italy, will not start serving their sentences until their appeals have been heard.
The so-called "no-TAV" movement against the rail link, which opponents say will wreck a pristine Alpine valley and potentially release toxic asbestos particles into the environment, has become a focus for the anti-globalization movement.
In June and July 2011, dozens of masked demonstrators fought pitched battles with police in the Val di Susa, the valley at the centre of the battle over the proposed TAV (Treno Alta Velocita or high speed train) between the French city of Lyon and Turin in northwest Italy.
France and Italy have both since reconfirmed their commitment to the link and drilling work for the new tunnel at the heart of the project began in 2013.
The project is expected to be completed in the late 2020s at a cost of at least €26 billion, around 40 percent of which will be provided by the European Union under a scheme to promote strategic cross-border links.
Supporters of the rail link say it will take a million lorries off Alpine roads each year once completed.
Critics, who have included France's public spending watchdog, have argued that the same result could be achieved with a far less costly upgrade of existing tunnels and rail tracks.
One third of the cost of the TAV has been allocated to building a new 57-kilometre (35-mile) tunnel under the Alps.
Tuesday's convictions came a day before Italian writer Italian Erri De Luca was due to go on trial in Turin for allegedly inciting criminal damage in two 2013 interviews in which he suggested it would be legitimate to sabotage work on the rail link.
The charges against him were initiated by the Franco-Italian joint venture established to build the link. Italian authorities have since backed the legal action against De Luca.