The 64km (40-mile) long construction will reach a depth of 40m (131ft) below and 6m above ground, at a cost of 3bn shekels ($833m).
An Israeli army commander said the barrier should be completed in 2019.
Israel has sought to neutralise the threat of cross-border tunnels since its war with militants in Gaza in 2014.
During 50 days of fighting, fighters from Gaza's ruling Hamas faction used tunnels to infiltrate Israeli territory on four occasions, killing 12 soldiers.
Israeli troops destroyed more than 30 tunnels and have found two since the end of the war.
The conflict left at least 2,251 Palestinians dead - including more than 1,462 civilians, according to the UN - and 11,231 injured. On the Israeli side, 67 soldiers and six civilians were killed, and up to 1,600 injured.
At a briefing on Wednesday, Israel Defense Forces (IDF) Maj Gen Eyal Zamir said the hi-tech barrier would be completed, even at the risk of renewed conflict with Hamas.
"If Hamas chooses to go to war over the barrier, it will be a worthy reason [for Israel] to go to war over. But the barrier will be built," Israeli media quoted him as saying.
Last year, Hamas's leader in Gaza, Ismail Haniyeh, said the group was still digging tunnels, without specifying whether these extended into Israel.
Part of the new barrier will protrude into the Mediterranean Sea, in an apparent effort to thwart attacks by frogmen.
Four such Hamas militants tried to swim out to attack an Israeli army base during the 2014 war, but were killed by the IDF.
According to local media reports, the machine used to dig the new the barrier will destroy any existing tunnels, while the barrier itself will use sophisticated technology to detect any new tunnels being built.