Azeri President Ilham Aliyev told a ceremony in the capital Baku that the project extension "will change the energy map of our region and help the historical development of our country".
The European Commission said the decision to go ahead with enlargement of the scheme could see it supplying 20% of European Union needs in the long term.
Gas shipments via Ukraine have been a focus of EU and Russian anxiety for years and especially since 2009, when a pricing dispute with Russia led to a cut-off of gas supplies to EU customers.
Since then, Europe has sought new suppliers and to bring Ukraine into its orbit, while Russia has fought to retain its influence over Kiev and to build alternative supply routes to safeguard deliveries to its European customers.
The documents signed in Baku include an investment decision on Shah Deniz II, as well as the Trans-Anatolian (TANAP) and Trans-Adriatic (TAP) gas pipeline projects. Combined, the projects will cost $35 billion (€25 billion), Aliyev said.
The European Commission welcomed the final investment decision (FID) on extracting gas from the Shah Deniz II gas field in Azerbaijan.
Commission President José Manuel Barroso is quoted as saying that the decision by the Shah-Deniz-II-Consortium “is a strategic door opener for stronger European energy security”.
Energy Commissioner Günther Oettinger was quoted as saying that the decision to open the Southern Gas Corridor “is a real breakthrough”.
“Through its further enlargement, the corridor will have the potential to meet up to 20% of the EU’s gas needs in the long term,” he added. The estimated gas consumption of the EU for 2011 was of 459.8 bcm/y, according to the CIA factbook.
Project partner Statoil of Norway accompanied its announcement on the go-ahead with news it would reduce its stake in the consortium to 15.5% from 25.5%.
Statoil's move will increase the ownership proportions of the remaining players and fits a trend among top oil companies to rein in spending by focussing on fewer big projects.
Statoil will sell the 10% to operator BP and Azeri state energy firm SOCAR for $1.45 billion in cash.
"It's a very good price ... The price is three times book value while Statoil shares are traded at 1.3 times book value," said John Olaisen, an analyst at brokerage ABG Sundal Collier in Oslo. Other analysts said investors would welcome the move.
An official statement by the consortium, which also includes Total, was expected later on Tuesday.
BP Azerbaijan and the consortium said SOCAR and its partners in Shah Deniz II had agreed to extend terms for the project by 12 years to 2048.
From around 2019, Shah Deniz II is expected to supply 16 billion cubic metres (bcm) per year to Europe, including 6 bcm for Turkey.
Alternative to Russia
European buyers have struggled to find alternatives to Russian gas producer Gazprom, whose contracts link prices to oil, generally making it expensive compared to the spot market.
Gazprom covers a quarter of Europe's gas needs, with more than 150 bcm of exports a year. In response to Europe's quest for Caspian supply, Gazprom proposed its $39 billion (€28 billion) South Stream project, which would pipe gas to northeast Italy through the Black Sea starting at the end of 2015.
The European Commission has said it does not oppose Russia's plans to diversify supply routes, bypassing Ukraine, but says they have to conform with EU law and are far from doing so.
"Shah Deniz II and the Southern Corridor pipelines will not only change the energy map, but will give customers in Europe direct access to the gas resources of Azerbaijan for the first time," Bob Dudley, BP's group chief executive, said at the signing ceremony on Tuesday.
Earlier this year, SOCAR and partners including BP and Statoil selected the TAP for potential gas deliveries to Europe over its Austria-based rival Nabucco West.
TANAP will be built from the Turkish-Georgian border to Turkey's border with Europe, with its preliminary total cost estimated at $20 billion.
Buyers of Azeri gas from Shah Deniz II are Shell, Bulgargas, Gas Natural Fenosa, Greek DEPA, Germany's E.ON , France's GDF Suez, Italian regional utility Hera Trading, Switzerland's AXPO and Italy's Enel.