outlook 365 C2R and moving Mailbox to CLoude

Hello

Could some one explain how outlook C2R E3 could support our moving mailboxes from on premise to the could?

shouldn't we have exchange on the cloud in order to be able to do that or our on premise exchange can support that?

Btw, We have about 2300 users that we need to move thier mail boxes to the cloud and we are looking for best office version that could support that.

Thanks