The traditional understanding of the history of agriculture begins in the ancient Near East and Southwest Asia, about 10,000 years ago, but it has its roots in the climatic changes at the tail end of the Upper Paleolithic, called the Epipaleolithic, about 10,000 years earlier.

It has to be said that recent archaeological and climate studies suggest that the process may have been slower and begun earlier than 10,000 years ago; and may well have been much more widespread than in the near east/southwest Asia. But there is no doubt that a significant amount of domestication invention occurred in the Fertile Crescent during the Neolithic period.
History of Agriculture Timeline
• Last Glacial Maximum ca 18,000 BC
• Early Epipaleolithic 18,000-12,000 BC
• Late Epipaleolithic 12,000-9,600 BC
• Younger Dryas 10,800-9,600 BC
• Early Aceramic Neolithic 9,600-8,000 BC
• Late Aceramic Neolithic 8,000-6,900 BC
The history of agriculture is closely tied to changes in climate, or so it certainly seems from the archaeological and environmental evidence.
After the Last Glacial Maximum (LGM), what scholars call the last time the glacial ice was at its deepest and extended the farthest from the poles, the northern hemisphere of the planet began a slow warming trend. The glaciers retreated back towards the poles, vast areas opened up to settlement and forested areas began to develop where tundra had been.

By the beginning of the Late Epipaleolithic (or Mesolithic), people began to move into the newly open areas northward, and develop larger, more sedentary communities. The large-bodied mammals humans had survived on for thousands of years had disappeared, and now the people broadened their resource base, hunting small game such as gazelle, deer, and rabbit. Plant foods became a substantial percentage of the food base, with people gathering seeds from wild stands of wheat and barley, and collecting legumes, acorns, and fruits. About 10,800 BC, an abrupt and brutally cold climate shift called by scholars the Younger Dryas (YD) occurred, and the glaciers returned to Europe, and forested areas shrank or disappeared. The YD lasted for some 1,200 years, during which time people moved south again or survived as best as they could.

After the Cold LIfted
After the cold lifted, the climate rebounded quickly. People settled into large communities and developed complex social organizations, particularly in the Levant, where the Natufian period was established. The people known as the Natufian culture lived in year-round established communities and developed extensive trade systems to facilitate the movement of black basalt for ground stone tools, obsidian for chipped stone tools, and seashells for personal decoration. The earliest structures made of stone were built in the Zagros Mountains, where people collected seeds from wild cereals and captured wild sheep.
The PreCeramic Neolithic period saw the gradual intensification of the collecting of wild cereals, and by 8000 BC, fully domesticated versions of einkorn wheat, barley and chickpeas, and sheep, goat, cattle and pig were in use within the hilly flanks of the Zagros Mountains, and spread outward from there over the next thousand years.

Why Would You Do That?
Scholars debate why farming, a labor-intensive way of living compared to hunting and gathering, was chosen. It's risky--dependent on regular growing seasons and on being families being able to adapt to weather changes in one place year round. It could be that the warming weather created a "baby boom" surge of population that needed to be fed; it could be that domesticating animals and plants were seen as a more reliable food source than hunting and gathering could promise. For whatever reason, by 8,000 BC, the die was cast, and humankind had turned towards agriculture.