Under the $893 million deal, IHI Corp. and Mitsubishi Electric will manufacture engine and radar parts.
Mitsubishi Heavy Industries will lead the final assembly process, Japan's Kyodo News reported.
MHI gets the lion's share of the work, worth about $651 million. IHI will get $185 million worth of work and Mitsubishi Electric's share will be worth about $57 million on the 42 aircraft on order.
The contracts follow the government's decision announced in March to allow local companies to join F-35 parts production.
Chief Cabinet Secretary Yoshihide Suga said at the time that Japan will uphold its long-standing ban on arms exports, the Kyodo report said.
But Japan would allow domestic companies to make parts for the F-35 only on the grounds the United States controls shipments.
Japan's Ministry of Defense selected the F-35 Lightning II on Dec. 19, 2011, following the F-X competitive bid process.
Lockheed Martin said Japan selected the F-35A conventional takeoff and landing variant of the Lightning II through the U.S. Foreign Military Sales process.
Other F-35 variants to be manufactured include a conventional takeoff and landing aircraft for the U.S. Air Force and allied air forces, a short takeoff and landing fighter for the U.S. Marine Corps and the United Kingdom's Royal Navy and a carrier version for the U.S. Navy.
Japan also ordered two F-35 jets for delivery in March 2018 that will be used for pilot training in the United States.
All aircraft are scheduled for delivery by 2021.
A report by Japanese newspaper Asahi Shimbun in August said the U.S. government had authorized 24 components for the aircraft's engine and radar system to be produced in Japan.
Japanese-made parts will account for about 10 percent of the aircraft's value and the door has been left open for more parts and systems made in Japan.
Asahi Shimbun said the United States agreed to allow Japanese companies to supply a maximum of 40 percent of the components, but using more Japanese-made parts would push up the price for the aircraft by 50 percent.
For Japanese companies to manufacture more parts, the government and private sector would have to invest millions of dollars for tooling up factories.
The newspaper also reported that the Defense Ministry said IHI will manufacture 17 parts for engine fans and turbines, while Mitsubishi Electric will produce seven radar system components, including signal receivers.
Lockheed Martin's F-35 remains locked in battle with Boeing's F-15 Silent Eagle and EADS Eurofighter for a major, but delayed, 60-aircraft contract with South Korea for delivery starting in 2017.
After a last-minute rejection of a bid from Boeing last month, South Korea formed a task force to review the project's budget and restart bidding for an aircraft to replace its aging F-4s and F-5s over five years.
Boeing's Silent Eagle was the only aircraft to come in under the project's $7.2 billion budget.
Analysts have said the new procurement process is expected to favor Lockheed Martin's F-35, which scored the highest in combat capability.
South Korea's Defense Acquisition Program Administration's decision to reset the bidding was said to be, in part, over criticism it had focused too much on price, while overlooking skepticism over the F-15's stealth systems.
The U.S. Navy said in August that its first F-35C Lighting II was granted interim safe-for-flight status after a 1.5 hour maiden flight from the Eglin Air Force Base in Florida.
The Navy's variant has larger wings than other F-35 variants and has folding wingtips and other designs the company says make it suitable for naval aircraft carriers.
"The Lightning II strike fighter represents the future business end of our nuclear-powered aircraft carrier force," U.S. Navy Vice Adm. David Buss said in a statement.