The deal could face political controversy since Israel has used such bombs against the Palestinians.
In one such instance in July 2002, a one-tonne bomb meant for a senior Palestinian resistance fighter also killed 15 civilians in an attack in the Gaza Strip.
The deal is worth $319 million and was revealed in a Pentagon report made to the US Congress a few weeks ago, Israeli daily Haaretz said on Tuesday.
Funding for the sale will come from US military aid to Israel.
The bombs include airborne versions, guidance units, training bombs and detonators. These bombs are guided by an existing Israeli satellite used by the military.
As part of the deal, Israel will receive 500 one-tonne "bunker-buster" bombs that can destroy 2m-thick concrete walls, 2500 "regular" one-tonne bombs, 1000 half-tonne bombs and 500 quarter-tonne bombs, the daily said.
Known by the military designations GBU-27 or GBU-28, "bunker busters" are guided by lasers or satellites and can penetrate up to 10 metres of earth and concrete.
F-15 fighter jets have bunker
bombs fitted on by Israel
Israel may already have some of the bombs for its F-15 fighter jets, the paper reported.
"As they are part of the weapon set for the F-15, I would assume them to be in place," said Robert Hewson, editor of Jane's Air-Launched Weapons.The Pentagon wants the deal to maintain Israel's military advantages and ensure US strategic and tactical interests, Haaretz said.
Acquiring BLU-109s, which are mounted on satellite-guided bombs, would boost Israel's capabilities, foreign experts say.
"Israel very likely manufactures its own bunker busters, but they are not as robust as the 2000lb (910kg) BLUs," Robert Hewson, editor of Jane's Air-Launched Weapons, said.
The US embassy in Israel had no comment, referring queries to Washington. Israel's Defence Ministry also declined to comment.
He said the bombs proved effective in the 1991 Gulf war and the more recent US-led invasion of Iraq.
Bombs for neighbours?
Haaretz said Israel sought to obtain the US-made, one-tonne "bunker-buster" bombs for a possible future strike against Iran or Syria.
A senior Israeli security source confirmed the Haaretz story saying: "... bunker busters could serve Israel against Iran, or possibly Syria".
"Our response to any invasive measure will be massive"
spokesman for Iran's Revolutionary Guard
"Our response to any invasive measure will be massive," Massoud Jazairi, spokesman for Iran's Revolutionary Guard, said in Tehran.
Iran, which does not recognise Israel's right to exist, says its nuclear programme has only peaceful purposes to meet its growing energy needs.
An Iranian Defence Ministry spokesman said the disclosure of a US-Israeli deal could be "psychological warfare to test us ... This relationship has a long history. The United States has given Israel more advanced weapons than this."