It is not clear from your sentence whether you mean past or present tense.


Using your words (past tense):

I emailed you as you asked me to inform you of any progress he has made.

Using your words (future tense):

I will email you as you asked me to inform you of any progress he makes.

Other options:

As requested, I have emailed you to inform you of his progress.

As requested, I will email you to inform you of his progress.