Here's the history of the penny from the US Mint Site
--The composition was pure copper from 1793 to 1837.
--From 1837 to 1857, the cent was made of bronze (95 percent copper, and five percent tin and zinc).
--From 1857, the cent was 88 percent copper and 12 percent nickel, giving the coin a whitish appearance.
--The cent was again bronze (95 percent copper, and five percent tin and zinc) from 1864 to 1962.
(Note: In 1943, the coin's composition was changed to zinc-coated steel. This change was only for the year 1943 and was due to the critical use of copper for the war effort. However, a limited number of copper pennies were minted that year. You can read more about the rare, collectible 1943 copper penny in "What's So Special about the 1943 Copper Penny.")
--In 1962, the cent's tin content, which was quite small, was removed. That made the metal composition of the cent 95 percent copper and 5 percent zinc.
--The alloy remained 95 percent copper and 5 percent zinc until 1982, when the composition was changed to 97.5 percent zinc and 2.5 percent copper (copper-plated zinc). Cents of both compositions appeared in that year.
So it looks like 1982 on is when it has been majorly zinc.