Aasgaard is Matt Bloomfield’s second signing since his appointment as Hatters manager on 14 January, following the return of defender Kai Naismith for a second spell at Kenilworth Road on loan from Bristol City for the rest of the season.
Second-bottom Luton have taken one point from their three games under former Wycombe Wanderers boss Bloomfield, losing their most recent two at Oxford United and at home to Millwall.
“He’s a player who I’ve had my eye on from afar for a while,” Bloomfield said of Aasgaard.
“He’s technically very, very good and can create and score goals. Thelo can play as a 10 but can play as an eight or on the left, so he’s adept at playing in a variety of positions.
“The board has been incredibly supportive in this process and I’d like to thank them for making Thelo’s signing a reality.
“He’s a player who will add immediate quality to the group and also comes with lots of potential, so we’re looking forward to seeing what he can do as a Luton Town player.”
Aasgaard could make his debut for Luton, who are three points from safety, when they visit Sheffield Wednesday on Saturday (15:00 GMT).