There is no" 我吃過” in Chinese.
Actually it is totally same in Chinese, and its just a bit different when we native Mandarin speaker say it.
We use "我吃了” when people ask "Have you eaten ~"
We use "我吃過了” when people ask " Do you like to have some~ (foods)"
Ex:
A:你吃了嗎?
B:我吃了。
A:你要吃麵嗎?
B:我吃過了。