Singleplayer and Multipler using Direct Connect are unaffected. The issue is affecting multiple users, there is a thread on Reddit relating to it. https://www.reddit.com/r/realms/comments/3y9o6x/invalid_session_id_opening_up_realms_list/
I have restarted Minecraft, my PC and even removed all the files in the Versions folder and redownloaded and i still have the same problem.
Completely ignored arguments: [--nativeLauncherVersion, 286]
[10:11:41] [Client thread/INFO]: Setting user: Jay_Wall
[10:11:41] [Client thread/INFO]: (Session ID is token:220b6c444c9b48d3a36f0ae79734afee:62af0b7497a54b39809ea7072fb5e8d0)
[10:11:41] [Client thread/INFO]: LWJGL Version: 2.9.4
[10:11:42] [Client thread/INFO]: Reloading ResourceManager: Default
[10:11:42] [Sound Library Loader/INFO]: Starting up SoundSystem...
[10:11:42] [Thread-6/INFO]: Initializing LWJGL OpenAL
[10:11:42] [Thread-6/INFO]: (The LWJGL binding of OpenAL. For more information, see http://www.lwjgl.org)
[10:11:42] [Thread-6/INFO]: OpenAL initialized.
[10:11:42] [Sound Library Loader/INFO]: Sound engine started
[10:11:43] [Client thread/INFO]: Created: 512x512 textures-atlas
[10:11:44] [Realms Notification Availability checker #1/INFO]: Could not authorize you against Realms server: Invalid session id
[10:11:58] [Client thread/INFO]: Realms library version == 1.7.48
[10:11:58] [MCO Availability Checker #1/INFO]: Could not authorize you against Realms server: Invalid session id
[10:11:58] [MCO Availability Checker #1/ERROR]: Couldn't connect to realms:
I have the same problem. There are also users on Reddit reporting the issue. Get out of bed Mojang!
Do you have an update to this please?