The project has a total budget of 62.9 million euros and is being implemented by a consortium of four construction companies. The fence will be 27 km long, and eight observation posts will be built for the Greek army.
The existing fence, which was damaged in 2015, will be reinforced with steel structures 4.3 m high, instead of the current 3.5 m.
Greek Prime Minister Kyriakos Mitsotakis will visit Evros over the weekend to inspect the construction.
Earlier UK Interior Ministry appealed for help to the army, as well as to the French government to curb the migrants' flow. This was reported by Reuters.
Taking advantage of the hot weather and calm sea conditions, hundreds of people, including children and pregnant women, have crossed the dangerous 33 km sea route in overloaded rubber boats in recent days.
The UK Department of Defense has received an official request from the Home Office to send military forces to assist border guards in operations in the Strait of Dover.
UK Immigration Secretary Chris Philp tried to put pressure on France ahead of meeting with his French counterpart in Paris.