In order to take advantage of the delivery service provided through FedEx, you'll have to be enrolled in text alerts from Walgreens. The service sends a text message to you when your prescriptions become available. Through the same service, you'll be able to ask to have the medication delivered to your doorstep.

Walgreens' partnership with FedEx comes as Amazon's prospective presence in the prescription drug game is looming. Last year, the online retail giant started mulling the idea of selling medication through its marketplace. Earlier this year, Amazon took a step closer to making that a reality when it bought online pharmacy company PillPack. Amazon already has the infrastructure in place in many locations to provide next-day and same-day delivery should it finally do more than dip its toes into the prescription drug market.