We have Exchange 2010 SP3 on premises. We want to deploy online archiving. Actually we have EOP but we add users to it manually.

I Known we need a Hybrid Deployment. Also, I found this on TechNet "Active Directory synchronization between the on-premises and the Office 365 organizations is a requirement for configuring a hybrid deployment"....

Then...is it necessary deploy a Synchronization server for Exchange Online Archiving ??

I think that DirSync Server is necessary to synchronize some attributes:

msExchArchiveGuid
msExchArchiveName
msExchElcMailboxFlags
msExchRemoteRecipientType

Hi,

For your question, here's an article about Configure Exchange Online Archiving in Exchange 2010:
https://technet.microsoft.com/en-us/library/hh529915(v=exchg.141).aspx

Note: If you don't want to confirgure full hybrid deployment, you can refer to below deployment checklist document:
To configure a limited hybrid deployment with single sign-on, download the following document: http://go.microsoft.com/fwlink/p/?linkid=248654
To configure a limited hybrid deployment without single sign-on, download the following document: http://go.microsoft.com/fwlink/p/?linkid=248653

Hope it will help.

Those URLs don't resolve my doubt...

Is it necessary deploy a Synchronization server for Exchange Online Archiving (with on-premises mailboxes) ??

Hi,

Yes, we need Directory Sync tool to sync local AD with the Office 365 service. However, if you want to deploy SSO(single-sign-on), please deploy it first with AD FS.

Please refer to "Hybrid deployments with multiple Active Directory forests" section in below link:
https://technet.microsoft.com/en-us/library/jj873754(v=exchg.150).aspx