The information can be circulated by various means. If the resignation is accepted you can circulate through Email, Inter office note or word of mouth. It depends on you, if in case if you have a replacement for that post, you can send that person's name also for better understanding.
2nd December 2013
The team members, of the resigned person, may be curious to know the reason for his exit. An employee may be leaving for better prospectus, or for job abroad, or for starting his own business, or shifting residence to other city, etc. etc. You can put a single line in the communication mentioning the reason, in good way.
Also, depending upon the the association of the employee with the organization, if company is having a policy of offering farewell to going person, you may make mention about the same, in the communication.
3rd December 2013 From India, Mumbai