Earl signed a one-year deal with the Hatters on Monday after leaving former club Preston and will immediately be loaned out to the New Bucks Head.
The 19-year-old offers plenty of options to manager Gavin Cowan.
“Lewis is versatile, he plays as a defender but also as a midfielder as well, so we are really lucky," said the Bucks boss.
“I’d like to give a real huge thanks to Stockport, who have seen the bigger picture, from a financial perspective they’ve recognised that and allowed us to bring a player of his quality in.
"It makes our squad even more competitive and gives us strength in depth as well, so we’re really pleased.”
Cowan also remains confident of securing several other targets over the last few weeks.
“We do need that centre-half and a left-sided player as well, we’re hoping to bring in one or two, there’s no panic.
"I’m happy with the group at the moment and we showed how competitive we can be (on Tuesday), but we’re certainly in the market.”