I will keep you updated is a polite way to end a conversation about a new project or person. It's implying that should anything change, you will be informed.

How do you say I will keep you updated?

If someone asks you to keep them posted on the general progress of a project, you may want to say, “Ok. I'll keep you updated.” Alternatively, if they are waiting for some specific information you can say, “Ok. I'll let you know as soon as we hear something.”

How do you say just to update you?

Just to update you, I have done the work yesterday already. Hello, Just an update, I have done the work yesterday already. "Just to update you, I did the work yesterday".