Chiltern Pharmacy will begin operating from Morrisons in Verwood on Tuesday 1 September.
Pharmland Ltd, which also operates Verwood Pharmacy, was selected as the preferred bidder after Morrisons decided to sell several of its pharmacies.
The branch will remain in the same location, with its existing staff and usual opening hours. Its telephone number, 01202 826555, will also remain unchanged.
Patients will not need to change their prescription arrangements because NHS records will transfer automatically. However, the pharmacy has warned that delays may occur on Tuesday while its new prescription code is activated.
The branch will be closed for the bank holiday on Monday while new systems are installed.
The new system will send patients a text message when prescriptions are ready. Chiltern Pharmacy also plans to introduce more NHS and private healthcare services over the coming months.
More details about the sale of Morrisons pharmacies are available on The Pharmaceutical Journal website.