Yes, its safety has been approved by the U.S. Food and Drug Administration (FDA) and European Food Safety Authority (EFSA), as well as the Joint FAO/WHO Expert Committee on Food Additives (JECFA).  

FDA
Aspartame may be safely used in food as a sweetening agent and a flavor enhancer in accordance with good manufacturing practice. (17).


It was discovered in 1965 and was approved by the FDA 1981 in tabletop sweetener, hot beverages (coffee and tea), cold breakfast cereals, chewing gum and other related applications after more than 100 scientific studies. (18)

FDA approved its use in carbonated beverages in 1983. (19)

EFSA

Aspartame (E951) is listed in Commission Regulation (EU) No 231/2012 as an authorised food additive and categorized in “ Sweeteners” (20).

 

http://www.chinafooding.com/Aspartame