Which is correct? `He’s a teacher of English’ or `He’s an English teacher’?

Grammatically both are correct, but their meanings are somewhat different.
When you say that someone is a teacher of English what you mean is that the subject the individual teaches is English.
The sentence, `He is an English teacher’ is rather ambiguous. It could mean that the man teaches English. It could also mean that the teacher is English — in other words, the teacher is an Englishman.
Source: The Hindu ‘Know Your English’ Series, November 21, 2005.