O2, which has no relation to the UK-based telco, serves 370 customers, including Tabcorp, Sensis, Medibank Private and News Limited.
It is the fastest growing data network solutions provider in Oz, according to its website.
This latest acquisition is another move towards the telco's expansion of its network services, called Network Applications and Services (NAS).
The deal is believed to be worth $60 million, reports AFR.
"As our customers shift towards cloud-based environments, they increasingly require capabilities to securely integrate networks, data centres and cloud-based applications," said Telstra NAS Executive Director Michelle Bendschneider.
O2 significantly enhances this capability within Telstra's NAS portfolio.
The company is known for its deep-domain expertise and speed to market with emerging technologies including wireless network integration and next gen security threat detection solutions.
This latest purchase follows the telco's recent acquisition of NSC Group, as it embarks on a spending spree to advance its new cloud focused strategy, moving away from traditional telecom services.
O2 Networks Managing Director Euan Prentice said O2 and Telstra enjoyed a long-standing relationship and the combination is viewed as logical.
Telstra's NAS unit is certainly on the up.
The division increased revenue by almost 18 per cent last financial year, and signed a major $1.1 billion six year contract with the Department of Defence, Jetstar and Fitness First.
The O2 brand would be retained for the time being and all O2 staff will continue to be employed by Telstra after the acquisition. The acquisition is complete and was not subject to ACCC approval.