Manager Vincent Kompany made Benson, a Belgium international at under-21 level, his 10th summer addition.
The 25-year-old arrived in Lancashire from Royal Antwerp, where he won the Belgian Cup back in 2019/20.
Burnley kicked off the season with a 1-0 victory over Huddersfield last weekend, and Kompany will be intent on maintain their solid start to the season.
When asked about Benson, the manager said: "One v one, he's a threat. We talk about low blocks and it's harder for teams to make a low block against you when you have someone like him who can beat a man.
"In the final third, he's a goal threat, and he'll add the pace that we need to the team. At the business end of the pitch, these types of things are harder to coach.
"Someone like Benson I believe still has a lot of progression in him. He's going to give us an instinctive performance in the final third, and we need that."
Luton kicked off their season with a 0-0 draw at home against Birmingham last Saturday.
When asked about his opponents, Kompany added: "I've spent a lot of time watching them and they won't change the way they play because they're coming to Turf Moor, but as the season progresses, you have to earn the right for teams to come and sit deep. We're not there yet.
"Luton are a team with a lot of athleticism who manage to play to their strengths really well. There's clarity in what they do, and they're really good at what they do. That's the threat.
"Like in every game, we've had a look at what opportunities there are for us against them."