The US$114 million deal will see TEN Sports which is popular among cricket fans from the Indian sub-continent added to the Zee bouquet of channels.
This move will consolidate the number of sports broadcasters in the region and could cause a reduction in the burgeoning fees that they have to pay for sporting events.
Chris McDonald, chief executive officer of TEN Sports, said: "By coming together we can put a cap on, or even drive down, rights fees if there are fewer players bidding.
"Internationally, there is a Zee bouquet of channels, including in the Middle East. By combining TEN Sports with that bouquet, we can also drive a better deal for ourselves with any cable operator."
Subhash Chandra, chairman of Zee Telefilms, added: "This acquisition is an important step for Zee towards consolidation in the media industry. It not only gives us a strong foothold in the arena of sports broadcasting across Asia but also strengthens our operations in the Middle East."
TEN Sports operates separate beams for the Middle East, Pakistan, Sri Lanka, Bangladesh and Hong Kong.
The acquisition means TEN Sports' broadcaster, Taj TV, will have access to Zee's studios in India, which will enable it to broadcast more studio-based programmes, such as chat shows.
"This will make our channel here in the Middle East stronger," said McDonald. "The love of sports is growing, and these types of shows will become more viable."
The two channels will also be sharing their programming, enabling TEN Sports to broadcast football from India, for example, which is popular among expats from the southern Indian state of Kerala living in the Middle East.
McDonald added: "The market here is growing rapidly, especially with the South Asian expatriates moving here, and the population growing. They all want sport that reflects their culture and interests."
TEN Sports was launched in 2002 and is available in nearly 50 million cable and satellite households worldwide.
Zee already has a presence in the Middle East through its regional arm Real Media. The network has a dedicated Middle East beam for Zee TV and Zee Cinema.