The voracious CVS Health is already a dominant player in nearly every corner of the health care world — it is the nation’s largest dispenser of prescription drugs, the biggest operator of health care clinics and the second-largest pharmacy-benefits manager.

And with the news Monday that it had agreed to buy Target’s pharmacy and clinic businesses in a deal worth about $1.9 billion, it demonstrated that its appetite shows no signs of abating.

“CVS Health is building a business that has a lot of interlocking synergies in many different parts of the health care system,” said Adam J. Fein, president of Pembroke Consulting, a management advisory and business research company based in Philadelphia. “The Target deal is one more step in their goal of becoming the most significant company in the drug distribution and reimbursement system.”

Under the terms, CVS, which is based in Woonsocket, R.I., would acquire more than 1,600 pharmacies from Target in 47 states and operate them under the CVS name in Target stores. CVS will also operate branded pharmacies in new Target stores that offer pharmacy services.