YES, absolutely. According to the FDA, all FDA-approved generic medications have the same active ingredients and the same strength as the brand name versions, and they work in the same way. As a result, they will have the same benefits and risks as the brand name versions, meaning they will be equally effective and equally safe.
The inactive ingredients, however, CAN be different in a generic version of a medication, so if you have allergies or intolerances, be sure to read the inactive ingredients list.
A big benefit of generics is that they're much less costly if you have to pay out of pocket for your birth control.
Lots of birth control brands have generic equivalents, including many birth control pill brands, emergency contraception pills, and hormonal IUDs.