Jones had passed away due to a cardiac arrest in Mumbai on September 24.
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The tribute was paid during the opening day of the Boxing Day Test at the iconic Melbourne Cricket Ground (MCG).
Jones' family and former Australia skipper Border participated in the farewell during the tea break of the ongoing second Test.
According a PTI report, they took a long walk from the MCG boundary to the centre, carrying Jones’ baggy green, sunglasses and Kookaburra bat and laid the items to rest on the stumps at the Great Southern Stand end of the ground.
The report also says that the 12th men from both sides – KL Rahul (India) and James Pattinson (Australia) – collected the items and rested them on a seat by the boundary.
The gesture was applauded by the 30,000 spectators present at the MCG.
"It's quite fitting the tribute was done during Australia vs India. He's loved over there," Former Australia speedster Brett Lee, who was with Jones during his final hours in Mumbai, told Fox Sports.
Jones played 52 Tests and 164 ODIs for Australia and was inducted into the Australian Cricket Hall of Fame last year. He also featured in the 1987 World Cup-winning Australian team.
(With PTI inputs)