Souq.com, which sells consumer electronics, fashion, household items and other goods, is one of the best-known names in the Middle East's online shopping market and lays claim on its website to being the largest e-commerce site in the Arab world.
E-commerce in the Middle East is expanding quickly due to the region's young and tech-savvy population. Kuwait, Saudi Arabia and the United Arab Emirates are among the top worldwide for mobile phone penetration.
Amazon declined to comment and a spokesperson for Souq.com did not immediately respond to a request for comment.
Goldman Sachs acted as adviser for Souq.com and helped to arrange the deal, two of the sources said.
The sources didn't disclose the price Amazon and Souq.com have agreed on.
Souq.com had according to media reports been valued at $1 billion at the time of a funding round last year, but the sources say that valuation has since dropped.
One of the sources close to the deal said it gave Amazon a presence in the region without having to deal with bureaucratic hurdles such as getting regulatory approvals from each region and signing up vendors and suppliers.
"Amazon acquires business that they see as tangential to the core e-commerce marketplace, and in this case, I assume what they gain with Souq.com is a strong local brand, an early leadership position in the Mid-East e-commerce market, and a team with plenty of local expertise," Baird Equity Research analyst Colin Sebastian said via email.
"Jeff Bezos and Amazon are clearly interested in tapping into growth in emerging markets they recently launched in Mexico, they are investing billions in India, and it probably makes sense in other markets to make an acquisition."
Souq.com launched in 2005 as an Internet auction site and has developed into a retailer and marketplace for third-party vendors, serving a number of markets in the region, including UAE, Egypt, Saudi Arabia, Kuwait, Bahrain, Oman and Qatar.
Last year Souq.com raised $275 million from a funding round with investors to support its future growth. Investors participating in that funding round included Tiger Global Management, Naspers, Standard Chartered Private Equity, International Finance Corporation and Baillie Gifford.
Interest is growing in the region's e-commerce market, estimated to be worth $20 billion in 2016.
Last year Emirati businessman Mohamed Alabbar teamed up with Saudi Arabia's Public Investment Fund (PIF) and other private investors to launch a $1 billion Middle Eastern-focused e-commerce platform.