"I spoke to Clarke and he said to me that he hoped the politics of the situation wouldn't get in the way of his welfare and I thought that was a fair thing to ask," manager Adrian Boothroyd told the clubs official website.
"Clarke has been playing reserve football, but nothing replicates first team action and both Watford and Clarke need him to be playing games at a good standard.
"The main thing is that this deal will benefit Clarke and it will benefit Watford while will get the services of a great player for a short time.
"He will get five games under his belt with Luton and will come back to us a match-fit player."