Councillor Emer Costello says the move "will bring improvements to the area".
However, she expressed her concern at the fact that no owners were notified by letter about the ACA by the DCC.
Under the conservation order, owners will need planning permission if they are to change their advertising signs.
"The practice of advertising that turns shop fronts into bill boards is not desirable," it is stated within the ACA report.
The report says banner-type signs and advertising sheeting covering any part of the front facade of a building in the street are not acceptable.
It adds: "Careful consideration should be given to the colours used on any advertising structures or signs.
"Substantial areas of inappropriate garish colours shall not be allowed as the background of any sign."
Many locals have welcomed the move as it will enforce tighter planning controls on shop owners along the street, which is lined with charity shops, adult stores and ethnic supermarkets.
Capel Street was built in the early 18th century.