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

FDA
L-(+)-tartaric acid obtained from wine making is generally recognized as safe (GRAS) as a direct human food ingredient and can be used as a firming agent, flavor enhancer, flavoring agent, pH control agent and humectant in food with no limitation other than current good manufacturing practice. (4)

EFSA
L-tartaric acid (E334) is listed in Commission Regulation (EU) No 231/2012 as an authorised food additive and categorized in “Additives other than colours and sweeteners” (5).

Approved uses
E334 is listed in the group I which means most of its applications are not specific. The following food may contain with L-tartaric acid:

Canned or bottled fruit and vegetables
Jam, jellies and marmalades and sweetened chestnut purée
Cocoa and Chocolate products
Fresh (pre-cooked) pasta
Potato Gnocchi
Table-top sweeteners in tablets
Biscuits and rusks and baby foods for infants and young children
UK Food Standards Agency
Categorized in “Others” (6)

Food Standards Australia New Zealand
It is an approved ingredient in Australia and New Zealand with the code number 334. (7)

JECFA
Function Class: food additives, flavouring agent, acid, antioxidant synergist, sequestrant. (8) (9)

Acceptable daily intake: Group ADI “30 mg/kg bw” set in 1977 for it and its salts of sodium, potassium, and potassium–sodium. (10)

http://www.chinafooding.com/L-Tartaric_Acid