History

The Amazon rainforest has been in existence for at least 55 million years, with its formation dating back into the Eocene era. After the Cretaceous-Paleogene extinction event, the absence of dinosaurs and wetter climate caused the spread of the rainforest across the continent. It expanded again during the Middle Miocene era, but retraced during glacial periods (4).

The Eocene era, when the rainforest was formed.
http://www.corzakinteractive.com/earth-life-history/432_eocene.htm

When the continents existed as Gondwana, the Amazon river flowed Westward towards the Pacific Ocean. However, 15 million years ago, when the Andes were formed, the rise of the Andes and the collision of Brazilian and Guyana bedrock blocked the river and caused the Amazon to become an inland sea. It then resembled a swamp-like, freshwater lake (4).

The continent of Gondwana
http://historyoftheearthcalendar.blogspot.com/2014/05/may-15-devonian-gondwana.html

The formation of the Andes
http://www.geocaching.com/geocache/GC1EZDD_cajas-national-park?guid=f0b5ae69-c032-4845-aee6-4aef0242ddec

10 million years ago, water from the river worked its way through the sandstone and began to flow East. When the Ice Age occurred, sea levels dropped, the lake drained, and the river was once again formed. The low temperatures transformed large areas of the Amazon into Savanna and Montane forest, which divided the rainforest regions into individual "islands." When the Ice Age ended, the forest rejoined and the Amazon rainforest began to resemble the rainforest that exists today.
In the last 21,000 years, there is evidence that much of the vegetation in the rainforest has been changing due to the Last Glacial Maximum and deglaciation (4).

The Amazon rainforest today.
http://www.shedexpedition.com/amazon-rainforest/