Must remember that the language that the Ottomans spoke,Osmanlica(or maybe called Osmanli)was a mixture of Turkic with a lot of Arabic and Persian words.During Ataturks reign,he had his people to clean up the language of Arabic and Persian words.
Today,the official language of Turkey that we call Turkish is mostly cleared of Arabic and Persian words,but from what I've read it includes thousands of foreign words of various languages which have been altered to sound Turkic.
Also remember that the Seljuks,as the first Turkic power to arrive in Anatolia,spent a great deal of time in Persia and Arabia before coming to Anatolia,so it's no suprise that the language they spoke included many Arabic and Persian words.Also,a lot of the Central Asian Turkic people's culture is Persian or Indo-Iranian.