A trade deal 25 years in the making between Europe and South America is nearly over the finish line

Talks on a landmark free trade deal between the European Union and four South American countries started so long ago that the euro wasn’t even in circulation, China hadn’t yet joined the World Trade Organization and Venezuela was still America’s top oil provider.

But against a starkly different geopolitical background and tough odds — including backlash from powerful protectionist lobbies — the EU and the South American alliance known as Mercosur are expected to formally sign their quarter-century-in-the-making...