Are you talking about the Vinland sagas?

These are stories about a guy "Erik the Red" who was thrown out of Norway for being a murderer. He settled in Iceland for a while and got into more trouble, which encourages him to seek new land to settle.

The two books you want are: "Saga of the Greenlanders" and "saga of Erik the Red"

There has been research into the contents of these stories, and there is archeological evidence of a Norse settlement at L'Anse aux Meadows in Newfoundland which is dated to the correct time period.

But I think it would be incorrect that it was "greenlanders" who did the exploration...