Actually, its both. Old English is related to Old Norse as modern German is to modern Swedish: They're similar but not as close as German and Dutch or English and Frisian, for instance.
However, in the Early Middle Ages English was also heavily and directly influenced by Old Norse because Vikings at that time not only more or less continually invaded the English east coast but also settled and established their own jurisdiction (The Danelaw) there.
And it gets another dose after 1066 because the Normans were really former Vikings who adopted a Romance language and the Norman language contains a lot of Norse words in addition to Latinate ones.
