The governments of Albania, Greece and Italy stated support this week for the planned natural gas pipeline. TAP could move as much as 350 billion cubic feet per year to Europe from Azerbaijan.
EU Energy Commissioner Gunther Oettinger said the pipeline is "instrumental" to European energy security.
"It could be among the first components of the Southern Corridor, which aims at linking directly the European Union with the rich gas sources in the Caspian region," he said in a statement.
Europe aims to break Russia's grip on the energy sector with the Southern Corridor, a network of pipelines planned for alternative natural gas supplies. Russia supplies about one-quarter of Europe's gas.
A BP-led group working in the Shah Deniz gas field offshore Azerbaijan is expected to choose between TAP and the larger Nabucco West project by June.
TAP External Affairs Director Michael Hoffman said the trilateral agreement is one of the last hurdles before the June decision from the Shah Deniz group.