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Bolelli and Vavassori, the fourth seeds, dominated from the outset.
The season-ending tournament will be held at Turin from November 10-17.
The 44-year-old Bopanna had also lost in the men's doubles.
The second-seeded Bopanna-Ebden pair lost to the 16th seed Argentine combo of Maximo Gonzalez and Andres Molteni in 66 minutes.
Bopanna and N Sriram Balaji had lost to the French duo of Edouard Roger-Vasselin and Gael Monfils in the men's doubles first round.
The second seed Indo-Australian pair lost 5-7, 6-2, 2-6.
They beat last year's finalists Sander Gille and Joran Vliegen in three sets.
The 44-year-old Bopanna wrote to the AITA and also marked TOPS in the mail, conveying his decision - a development confirmed by the national federation.
The World No 1 defeated the Argentine 6-1 5-7 3-6 7-5 6-3 to reach the quarterfinals.
The Brazilians made life tough for the Australian Open champions who scraped through in two hours and seven minutes.
Results 1-10 of 53
