AuthenTec's fingerprint recognition and near field communications (NFC) software is used in various smartphones and personal computers.
The company only recently agreed a deal with Apple's fierce rival Samsung Electronics, involving the AuthenTec QuickSec VPN security software coming to future Samsung Android phones and tablets.
Apple's $8 per share offer for Melbourne, Florida-based AuthenTec was disclosed in a filing with the US Securities and Exchange Commission. It is thought to be worth around $356m (£225.9m).
Based on yesterday's (July 26) closing share price for the company, $5.07, the deal represents a premium of 58% for AuthenTec's shares, indicating that Apple was very keen to bring the technology in-house.
AuthenTec, which also has Lenovo, Fujitsu, and Dell among its clients, has annual revenue of only about $70m.
This has led to speculation that Apple will roll out various biometric features on its iPhones and iPads in future, enabling users to more easily maintain security on their devices.
Alongside fingerprint authentification software, AuthenTec also makes technology that enables users to securely access virtual private networks (VPNs), which could help Apple in the lucrative corporate market.
RIM's BlackBerry dominates the business market partially due to its security features, and it would be a big selling point for Apple if iPhones and iPads could securely link to corporate networks.