The defender, 19, has yet to make his Lions debut but has appeared on the bench three times this season, including in the FA Cup win at Kenilworth Road in February.
"I've seen quite a bit of Jake and I like him. Millwall like him. In fairness when I asked about him I didn't think I'd get him," said new Luton manager John Still.
"He's got a bit of pace, he's mobile, he can head it, he's got a great attitude, he's young, hungry and enthusiastic."
Goodman will make his Hatters debut at Nuneaton on Tuesday night.