The line, which is due to be completed by 2023, would allow high-speed trains to link Paris and Turin in just over four hours, compared to seven at present.
The Lyon to Turin connection would be cut back from just over four to just under two.
Work will begin with the digging of a 57-kilometre tunnel (35 mile) tunnel under the Alps to link the border areas.
The €8.5 billion ($11.2 billion) tunnel will funded by France, Italy, and the European Union, with Italian Deputy Transport Minister Mario Ciaccia saying he hoped the EU would pay 40 percent of the cost.
The new line will take account of human and environmental impact studies on the Italian side of the border where violent protests took place last year, French Transport Minister Thierry Mariani said.
Last week some 40 people were arrested, with 26 of them detained, following violent protests in July over the project.
"A minority cannot upset a shared decision, along with a national and EU programme," Ciaccia said, vowing to stand by the agreed timetable for building the link.
Early work to clear the way for the line started last summer in Italy's northern Susa Valley amid a strong police presence as protesters sought to break through barriers erected around the controversial site.
Susa Valley residents fiercely opposed the plan, saying construction of tunnels would damage the environment.