The index climbed after gaining 0.1 percent in April and 0.4 percent in May, the economic research firm said.
The index is a comparison to the average monthly index in 2004, which was assigned an index value of 100. For the eurozone, the index now stands at 107.5.
For the region, the index has made gains in five of the past six months.
"June saw the Leading Economic Index for the eurozone rise for the third straight month, increasing the odds for a recovery in the second half of 2013," said Bert Colijn, economist for Europe at The Conference Board.
"Even as business and consumer confidence grows, however, continued financial stability in the Euro Area remains vital for economic growth. Any renewed uncertainty would be a large setback for a recovery," Colijn said.