Season 1 episode 10, Memories of Boom Boom Mountain, is where it is first revealed that Finn was adopted by Jake's parents:
This triggers the last part of the "boom boom" memory. Finn is still stuck to a leaf when Joshua and Margaret pass by and see him there. The two dogs resemble Jake, for they are Jake's mother and father. Margaret kisses Finn on the cheek, which makes Finn feel better.
This is the first appearance of Jake's parents (see here):
Joshua first appeared with his wife in one of Finn's flashbacks in the episode "Memories of Boom Boom Mountain." They find Finn after he has soiled himself causing him to be stuck to a leaf. Finn claims to have cried for a whole day before anyone helped him. They are the second to stop, after a ladybug mum and daughter, and help the seemingly abandoned baby Finn. They take him to what is presumably their house and raise him as their own.