To be up to code, you will need to run that ground back to the fuse/circuit breaker box, where it will bond with the neutral. You can use #14 awg for 15 amp circuits and #12 for 20 amp circuits. Some people will tell you it can be smaller, but to properly protect , the grounding conductor needs to be able to handle the full current capability of the circuit, lest it act as a fuse during an incident.
I would use a green insulated wire and what are known as "pigtails" to do the connections. This is a short length of green wire with a green grounding screw. Be sure the grounds are either Green insulated, Bare wire, or marked with green electrical tape if another color of wire is used. This way any other person working on the boxes will know what each conductor is supposed to be.
Pigtails and Green wire nuts will allow you to make sure the ground is attached to both the outlet and the box.
Make sure you staple the ground wire securely no more than 8 inches from where it enters each box and no more than every 48" along any runs. The conductor does not really need protection from abrasion where it enters the box, as you WANT a connection between ground and the box, but it may raise some eyebrows, depending on who is doing the inspection, if you go to sell.
Some jurisdictions require a permit for ANY work that involves the panel. So if you may be selling, you may want to consider this.
HTH,
PM me if you need to.
Allen