ISTANBUL—A Turkish consortium on Friday won a $29 billion tender—the biggest in Turkey's history—to build and operate one of the world's largest airports in Istanbul, marking the most concrete sign of the country's ambition to become a global transit hub.

The group led by Limak Holding AS, a conglomerate with interests ranging from airport operations to construction and tourism, secured the right to run Istanbul's third airport for 25 years after bidding €22.2 billion ($29.1 billion) plus taxes. The five-company winning consortium,...