The 21-year-old made two Premier League appearances for the Hammers but featured only once this season, in the Capital One Cup defeat to Sheffield United in August.
Potts told Luton’s official website: “I can’t wait to crack on. Promotion is the key for me, I want success.
“West Ham’s a big club, but so is Luton and they want to succeed so in that respect the two clubs are no different.
“They have great fan bases and coming into the setup at Luton, will be good for me and hopefully we’ll push on and get up the leagues.”
Potts has also had spells on loan with Colchester and Portsmouth.