If you're referring to the Songs of the Return - I get the impression he likely died of his wounds. In Volume 56, where his death is mentioned, the campaign against the elves is still on-going.
Yep, here's the relevent passage:
The boy (Asgeir, as his name is now sung) had ran unimaginable distance at breakneck speed from the blood-stained fields of the Clouded Sun, to deliver the news to all who would hear. When he reached their camp, he bellowed a great sob before relieving his heart with the news that the mighty Ysgramor had breathed his last.