The motion, which was put forward by Chancellor Angela Merkel's governing coalition, passed with support from all the parties in parliament.
Turkey rejects the assertion that up to 1.5 million Armenians were killed in 1915 and instead says the number is much lower and does not constitute genocide.
It has prompted Turkey to recall its ambassador to Germany at a time when Ankara, is playing a key role in stemming the flow of migrants and refugees to Europe.
Turkish President Recep Tayyip Erdogan said: "This decision will seriously impact Turkish-German relations".
Church consultant and international lawyer Harry Hagopian, whose grandparents survived the violence, told Premier he was "fully aware that this was a difficult moment for Chancellor Angela Merkel".
He said: "If we look at what happened with the Holy See and the statement made by Pope Francis last year where he plainly spoke of the Armenian experience in terms of genocide it was only a little storm in a tea cup.
"After that things moved on as they had before."
He added there was a "sense of relief" that it vindicated history and his family which had survived the genocide.
Historians estimate that up to 1.5 million Armenians were killed by Ottoman Turks around the time of the First World War, an event viewed by many scholars as the 20th century's first genocide.
Turkey denies that the killings that started in 1915 were genocide and contends the dead were victims of civil war and unrest. Ankara also insists the death toll has been inflated.
Listen to Premier's Hannah Tooley speaking to Dr Harry Hagopian: