Tirion is just chilling there and then when we leave he walks up to the shoulders left behind and he picks them up. He says "The weight of such a burden, it must be mine. For there is no other." Then bolvar appears sitting on the frozen throne and all and tells him to put the shoulders on him. Thus making him the Warlichchiefking.
Then Tirion scrapes up the piles of nasty goo and guts left behind by Garrosh and puts it in a jar and hangs it on his wall.