Changed apple id and iCloud.

I had to change my apple id some time ago. On iCloud.com I also changed my id (which is my email address), but om my Mac the iCloud account still shows my old id. For example I can't use Key Chain now. How can I change my iCloud account on the Mac itself? I'm using a iMac, fall 2009, with OS 10.9.2 (latest version).

thx.