It is the first Australian telecommunications company to receive this certification.
The certification would expand the number of business applications compatible with Telstra's cloud computing services.
Executive director Philip Jones described the certification as the latest investment in its cloud offering.
Telstra is the seventh company to be certified, joining Amazon, Fujitsu, IBM, Ixonos, NTT Communications and Savvis.
Certification means a guarantee that existing Red Hat Enterprise Linux customers and firms who want to move to cost-effective Linux-based operating systems can run RHEL and supported applications and databases on Telstra's supported cloud platform.