The new development will be in Rosemount Road adjacent to the infirmary and is expected to be completed in six weeks.
The project will cost about £90,000, with £61,000 of funds provided by NHS Tayside.
About one third of the total cost is being made available from Arbroath Common Good funding.
The development follows an increase in outpatient clinics at the infirmary from 38 to 55 per week.
A new renal dialysis service has seen an increase in patients and visitors attending the hospital.
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The new car park is being created to deal with the increased pressure on car parking spaces in and around Arbroath.
NHS Tayside Chairman Sandy Watson said: "The Trustees of the NHS Tayside Endowment Fund, which I chair, recognise the benefit which this car park will provide for patients and visitors, and it is another good example of close partnership work between NHS Tayside and Angus Council."
Angus Council Depute Provost added: "It is some years ago now since I first raised at council this issue of hospital parking, so I'm delighted to see work beginning. The new car park will be of significant benefit to all those attending the hospital, whether they are staff, patients or visitors to the infirmary."
Angus Council says there should be minimum disruption to motorists during the work. Traffic management is needed to give access for works vehicles from Rosemount Road, but the rest of the work will be carried out from the existing park land.
(IT/CD)
