The transaction will strengthen Cognizant's offerings in the government and public health space.
"TMG Health will (now) enter into a new, expanded multi- year service agreement to continue providing IT, business process and other services to HCSC's various operating units and subsidiaries," Cognizant said in a statement.
The transaction is expected to close in the third quarter of 2017, it added.
No financial details were disclosed.
TMG Health, an HCSC subsidiary since 2008, has offices in Pennsylvania and Texas. It is a provider of BPO services to various medical support programmes in the US.
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