In Deathly Hallows, we witness Snape’s memory of his Sorting (and he was in the same year as them). We see Lily and the four Marauders all sorted into Gryffindor:
Then Professor McGonagall said, “Evans, Lily!”
He watched his mother walk forward on trembling legs and sit down upon the rickety stool. Professor McGonagall dropped the Sorting Hat onto her head, and barely a second after it had touched the dark red hair, the hat cried, “Gryffindor!”
The roll call continued. Harry watched Lupin, Pettigrew, and his father join Lily and Sirius at the Gryffindor table.
Alternatively, somebody else asked this exact same question in a 2004 interview with JKR:
What houses were Sirius Black, Remus Lupin, James Potter and Remus Lupin[sic] in? Everyone tells me they were all Gryffindor, but I won't believe it unless I hear it from Ms. Rowling herself!
JKR: This is JK herself saying that they were indeed in Gryffindor!
Yep, the Marauders were in Gryffindor.
(I’m assuming the second mention of Lupin was meant to be Pettigrew.)