Multiple stories seem to revolve around vikings adopting from outside their own culture. The most prevalent example are the Saxon Chronicles/Last Kingdom where a saxon boy is adopted by danes invading england. I've never seen any indication that this was an actual practice. Is this just a fictional trope or is it based in fact?
Not exactly the adoption, but the practice of fosterage to build a fictive kinship between the two families involved was widely known in Old Norse society, attested both by medieval Icelandic sagas and Scandinavian historical writings. The fictive kinship bonds the two families, especially the fostered-child and the forstering father, and makes them friends in a sense that they could rely on each other if the third party threatened the interest of at least one family.
As I commented in the thread, In A Song of Ice and Fire it is common practice for Lords to show their intent to honour treaties by fostering their children with other parties of the treaty. Was this common practice in medieval times?, the relationship created by this kind of fosterage often associated with the inequal (hierarchical) implication: The family that the fostered child came from was the superior status, the family of providing fostering household was the inferior one in such a case.
[Added]: Sorry for forgetting to answer 'how common' part. I'll give some examples from historical figures below:
I also wish to make a note that 'a (foreign) orphan adopted from out of the society' motif has actually been favored as a background of the protagonist by the author of the Saxon chronicle/ Lost Kingdom, Bernard Cornwell. To give another example, the protagonist of his other historical novel series, Warlord Chronicle (his retelling of historical Authur in post-Roman Britain), Derfel Gadarn, also turns out to be not in fact of the Britons.
Reference: