Morgan Stanley and Clifford Chance advised Actis on the transaction, which is subject to regulatory approvals.
EMP was established in July 2010 as a buy and build platform, to take advantage of increasing demand for payments infrastructure in Africa and the Middle East.
It serves more than 130 banks, 35,000 retailers, governments and consumer finance institutions across 45 countries in the Middle East and Africa.
The business allows banks to issue and process debit, credit and prepaid cards; make easier merchant acquiring; and offers retailer as well as e-government payment solutions.
EMP executive chairman Paul Edwards said: "Actis brought sector insight, local understanding and an unshakeable conviction to invest behind the thesis that Africa would welcome the very latest in payments technology.
"Since inception, EMP has delivered 30% p.a. growth and by combining forces with Network International we will be even better placed to grow further and meet the ever changing needs of our customers."
Actis has an increasing portfolio of investments in Asia, Africa and Latin America. It presently has $7 bn funds under management.
More than 40% of Actis’ investments are situated in Africa, with $3bn invested across 23 countries on the continent.
