Most of the 202 people who left Lesbos and Chios, and arrived at Dikili in western Turkey, are Pakistanis.
Under the deal, for each Syrian migrant returned to Turkey, the EU is due to take in another Syrian who has made a legitimate request.
Thirty-two Syrian migrants were the first to arrive in Germany from Turkey.
They were flown to Hanover in Lower Saxony, officials say.
The Greek authorities say 130 of those returned to Turkey on Monday were from Pakistan. There were 42 migrants from Afghanistan and others from Iran, Sri Lanka and Morocco, as well as several other countries.
Two Syrians were on board, and the Greek authorities insisted that those deported only included migrants who had not sought asylum.
The first returns were carried out calmly, Ewa Moncure, spokeswoman for the EU border agency Frontex, told reporters in Lesbos.
Activists staged small protests there and some shouted "No to deportations" and "EU, shame on you".
There was also a demonstration in Dikili.
Migrant crisis: Greece starts deportations to Turkey
05 April 2016
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The first boats carrying migrants being deported from Greece have arrived in Turkey as part of an EU plan aimed at easing mass migration to Europe.
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