The oldest anime I remember is Calimero. It originated from Italy and started airing in Italy on July 14, 1963. It later became an official anime in 1974.
Calimero (カリメロ Karimero) is an Italian/Japanese cartoon about a charming, but hapless anthropomorphized cartoon chicken; the only black one in a family of yellow chickens. He wears half of his egg shell still on his head. Source: Wikipedia
Calimero is a small black bird who has a shell on his head; his dream is to fly like the other birds. When he tries to fly and screws up he is teased by the other birds, but his girlfriend Pricilla is there to cheer him up. Despite his appearance, he is quite smart and thinks up an idea to fly. Source: MyAnimeList
Calimero originally appeared on the Italian television show Carosello on July 14, 1963, and soon became a popular icon in Italy. Therefore it was originally an Italian animation, but the characters were later licensed in Japan as an anime series, twice. The first was made by Toei Animation and ran from October 15, 1974 to September 30, 1975, and the second, with new settings and characters, was made in 1992. Altogether, 99 Japanese episodes were made (47 in the 1974 Toei series, and 52 in the 1992 Toei series).
Calimero officially became an anime in 1974 and it had international (outside of Japan) success in Italy in the 60's and in the Netherlands, Belgium, Germany and Spain in the 80's, so I would consider this to be the oldest anime I know of which was an international success.
The first series was also broadcast on European networks such as TROS (Netherlands and Belgium), ZDF and RTL II (Germany) or TVE (Spain).