The price for the stake represented an enterprise value of A$4.3 billion.
The transaction generated cash proceeds of $2.2 billion for CIMIC, above the previous estimate of $1.7-1.9 billion due to closing adjustments and the final financial position of the Thiess business.
Thiess is the world's largest mining services provider and the contractor will to deliver open cut and underground mining services in Australia, Asia, Africa and the Americas at 25 projects across a range of commodities, generating annual revenues of more than $4.1 billion.
CIMIC chairman and CEO Juan Santamaria said the sale would allow the company to capitalise on a strong sector outlook.
"The transaction proceeds will primarily be used to strengthen our balance sheet through the reduction of debt, while also providing additional capital to pursue organic growth prospects as well as broader capital allocation opportunities," he said.
"Our retention of the remaining 50% reflects the ongoing strategic importance of Thiess to our business."
CIMIC has a market capitalisation of about $7.5 billion.