ActivateClients specialises in applications and trading systems for the financial markets.
First Derivatives said the takeover would provide it with complementary software products.
This is the latest in a series of purchases by First Derivatives which now employs around 1,000 people.
Brian Conlon, chief executive of First Derivatives, said the latest deal was "a low-risk, earnings-enhancing acquisition for the company".
He added that ActivateClients would provide "additional technology capabilities, particularly in HTML5, and its staff possess software development skills that will be useful across a range of projects".
Pat Brazel, who was chief executive of ActivateClients, now becomes global head of software sales at First Derivatives.
Last October, First Derivatives paid £36m for a majority stake in a US software firm.
Kx Systems, which is based in Palo Alto, California, makes high performance databases using a technology called kdb+.
Its customers include banks such as Goldman Sachs and Morgan Stanley.
First Derivatives already held a 20% share in the firm, but the deal took its holding to 65%.
First Derivatives, the Newry-based financial technology firm, has bought a Dublin software firm for £3.4m.