Keeley, 22, has signed permanently with the Hatters.
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Luton manager Matt Bloomfield said: “Josh is a young, agile, athletic goalkeeper who had a great season last year in League One.
“He is an excellent shot-stopper and can play out from the back and sweep up behind the defence.
“We’re pleased to acquire a goalkeeper of his potential who already has plenty of experience.
“To be able to add someone of Josh’s pedigree and quality to the club is a real statement. He’s someone of big potential that we’re excited to add to our group.”