NHS Tayside has said that visiting may be resumed at its maternity units from July 13.
From Monday, pregnant women may identify one designated visitor to accompany them to scans and antenatal appointments.
They will also be able to identify one birth partner and one additional designated visitor to accompany them in labour, and on the postnatal ward.
Patients should identify one person to be their designated visitor for the duration of their pregnancy journey and hospital stay.
All hospital visitors must wear a face covering when accompanying a pregnant woman and should wash their hands before entering the hospital.
Anyone with any coronavirus symptoms should avoid attending and social distancing must be maintained as much as possible.
Children should not be brought to appointments or to visit.
Visiting on the postnatal maternity ward will be from 9am to 6pm.
Visitors may be asked to move to the ward day room or leave for a period of time if the midwife in charge of the shift assesses that there are too many visitors in one area.
Patients are asked not to arrive for scans or appointments more than five minutes before their allocated time to reduce the number of people in waiting rooms.
If the waiting room is busy, people will be asked to return to the department at a given time.
As visitors can come along to appointments, women will no longer be able to take a short video clip at the end of their scan.
Lead midwife, Lesley Sharkey, said: “We would like to thank everyone for their continued co-operation as we make changes to maternity services. Our main priority is to maintain the safety of women, their families and our staff.”