Translation:I am on the way.
"I am on my way" means "I am coming" (or "I am going", depending on the context). "I am on the way" does not mean "I am coming". It means that I am located on your way/route to somewhere. For example if you are travelling from Ankara to Istanbul via Eskisehir, then if I am in Eskisehir that means that I am on the way to Istanbul. You will be able to see me on the way to Istanbul. For it to mean "I'm coming" or "I'm going" you need to use the possessive pronoun. Same goes for "He's on his way", "You're on your way" etc..
I think this must depend on dialect: in mine, there's no difference between "I'm on my way" and "I'm on the way." If someone tells me "I'm on the way," I understand that to mean "I'm coming" unless the context indicates something different. Same with "I'm on my way." If someone says "I'm on [the/my] way to Istanbul," I understand that to mean that the person is en route to Istanbul.
I agree with you, saino. I'm a native English speaker. If someone phoned me while I was driving to their home, and they asked me, "Have you left yet?" I could answer either "I'm on my way" or "I'm on the way." Both these expressions mean I am presently heading toward them. And let's say my mother phones me while I'm riding on a bus to New York. "Have you reached New York, dear?" mom asks. I could answer: "Not yet, Mom. I'm on my way." Or "Not yet, Mom. I'm on the way." Both answers sound fine to my ears.