It will be the latest addition to hundreds of miles of fences and walls designed to keep out terrorists.
However human rights groups warned the fence might breach Israel's international obligations to accommodate refugees.
At least 17 people have been killed trying to cross the porous 150-mile border into Israel since May, most of them Africans shot by Egyptian police.
Announcing the £167 million) project, Benjamin Netanyahu, the Israeli prime minister, said: "This is a strategic decision to ensure the Jewish and democratic character of the state of Israel.
"Israel will remain open to war refugees but we cannot allow thousands of illegal workers to infiltrate into Israel via the southern border and flood our country."
Israeli police believe 100 to 200 people cross from the Sinai peninsular every week.
The new barrier will initially be built in two sections, one near the Red Sea city of Eilat and another on the edge of the Gaza Strip, where Egypt has already begun construction of an underground steel wall to close off smuggling tunnels.
The fence will include radar to detect human movement.
Eventually the whole border will be sealed.
Israel is also continuing to build its controversial barrier in and around the occupied West Bank. The government says the 400-mile system of fences and concrete walls is needed to prevent suicide bombers from launching attacks.
However, Palestinians, who often refer to it as the "apartheid wall", believe it is part of a land grab as some portions of the West Bank are contained within the Israeli side of the barrier.
There are about 15,000 asylum seekers in Israel, according to the United Nations Refugee Agency.
Eritreans fleeing national service and an oppressive government are the most numerous, along with others from Ethiopia and Sudanese escaping war-torn Darfur.
Some pay hundreds of dollars to Bedouin guides to escort them to the border, where a low fence separates Israel from Egypt.
There they face the risk of being shot by guards on either side.
Thousands more foreign workers have overstayed their permits. Many live in crowded slums in Tel Aviv or Eilat.
Refugees are a sensitive issue in Israel, a state established in part to absorb Jews fleeing persecution.
Itay Epstein, director of Amnesty International in Israel, said the barrier must not contravene international obligations to protect refugees.
"We congratulate the prime minister on his statement that he will not close the border to asylum seekers but we need to see a concrete policy that continues to allow access to the correct asylum seeking process," he said.
Tensions along the border between Gaza and Egypt have escalated in recent weeks.
The British MP, George Galloway, was deported from Egypt last week after leading an aid convoy into the Palestinian territory.
Days earlier activists clashed with Egyptian security forces and one soldier was killed after Hamas loyalists opened fire.
Palestinian militias in Gaza have meanwhile stepped up rocket and mortar attacks against Israel and faced return fire.
A spokesman for the Egyptian foreign ministry said the new barrier was purely a matter for Israel.
Israel to build security barrier on border with Egypt
Threaded Mode