The Haaretz daily reported that Barak will wrap up the contract at a ceremony Wednesday in Berlin with German Defense Minister Thomas de Maiziere.
The German government recently agreed after three years of negotiations to pay $178 million of the $659 million cost of the vessel, as requested by Israel.
Israel took delivery of three earlier-model Dolphin subs in 1998-2000.
Under Germany's policy of providing Israel with heavily subsidized weapons as part of a 1953 reparations agreement linked to the Holocaust of the Nazi era, Berlin donated the first two Dolphins to the Israeli navy.
It paid half the $700 million cost of the third of the diesel-electric boats, heavily modified versions of the Type-209 submarines developed by the Howaldtswerke-Deutchwe Werft AG shipyard in Kiel.
In 2006, Israel ordered two more boats during the administration of German Chancellor Gerhard Schroeder. Berlin agreed to pick up one-third of the cost of $1.27 billion of the more advanced subs.
The fourth sub, to be named the Tannin, Hebrew for "alligator," is scheduled for delivery by 2013.
The Israeli navy is already forming a 35-man crew for the boat, which it will take over from HDW, a subsidiary of the ThyssenKrupp engineering giant.
The fifth Dolphin, named the Rahav -- "swallow" -- is expected to be delivered in 2014 and the sixth, and most advanced, in 2016.
The 1,925-ton Dolphins are Israel's most expensive and advanced weapons platforms, and its most strategic, particularly in the context of a conflict with Iran.
The Islamic Republic doesn't have a nuclear weapon but it has a strategic force of Shehab-3b ballistic missile capable of delivering high explosive warheads to Israel and is developing the more advanced and longer range Sejjil-3.
All the Dolphins are reportedly capable of launching Israeli-developed, nuclear-tipped cruise missiles with a range of 950 miles through 650mm diameter torpedo tubes, carrying 200-kiloton tactical warheads.
That gives Israel an extended strategic reach, particularly if the missiles are launched from the Arabian Sea off Iran's southern coast.
It also gives the Jewish state, militarily the most powerful in the Middle East, the option of a pre-emptive first-strike attack by land, sea or air.
With six Dolphins, the Israeli navy will be able to maintain one, possibly two, of the boats deployed off Iran at all times.
IsraelDefense.com quoted a senior Israel defense official as saying the three new Dolphins, dubbed Super Dolphins, "have dramatically different capabilities than the existing ones, especially in their propulsion systems."
The subs under construction in Kiel will be fitted with a new system that combines a conventional diesel lead-acid battery system and an air-independent system used for silent cruising that makes it virtually undetectable by sonar.
The sixth submarine will be able to remain underwater for two weeks at a time, making it harder to detect, and "without the noise emitted by a nuclear sub which endangers its survivability."
The new boats will also have modifications specified by the Israeli navy, although these haven't been disclosed.
The first batch of Dolphins have a reported range of 2,800 miles but the newer ones have a larger fuel capacity that extends their range to around 6,250 miles and an operational endurance of 50 days, 10 days more than the original three.
In the meantime, the Israelis have reportedly become concerned about a fast torpedo Iran is supposed to have developed for its Russian-built Kilo class submarines, recently upgraded, and are reported to be developing advanced countermeasures.
The new Iranian weapon is supposedly reportedly modeled on Russia's VA-111 torpedo.
Israel's Rafael Advanced Defense Systems is reported to have developed deception and jamming systems, about which little is known.
One system that has been disclosed is the Torbuster, launched by a ship or sub, which activates some distance from its launch point and simulates a target. When the torpedo locks on and veers toward the false target, the Torbuster explodes and destroys the torpedo.