The low-cost carrier will operate both routes on a year-round basis with Venice flights running four times per week and Vienna services twice weekly.
Ali Gayward, easyJet’s head of Scotland, said: “We are pleased to further strengthen our network from Edinburgh with the addition of these services and are confident that Venice will prove a popular destination for travellers.
“We believe that the new Vienna route will prove a popular addition to our existing network with its magnificent historical architecture.”
EasyJet already serves Venice from Gatwick, Luton, Southend and Manchester, while it also flies from Gatwick, Luton, Manchester and Bristol to Vienna.