Craddock says he was aware of rumours linking him to several clubs, but took little notice until something became more concrete.
"I found out Oxford had made their interest known to Luton at the weekend and I couldn't wait to talk to the manager. Once I got to meet him I was keen to sign before the deadline came," he said.
The former Middlesbrough youth product was out of contract at Kenilworth Road at the end of this season and links up with former Luton team-mates Asa Hall and Simon Heslop.
"I spoke to Asa and also having played two games against Oxford last season, I knew that they had a lot of good players so I was pleased to able to come and join," he said.
"It's a three-year contract and in that time I hope we can have a lot of success. I can't wait to get into training on Thursday."
Boss Chris Wilder said missed opportunities in the Johnstone's Paint Trophy 2-0 defeat at Aldershot underlined why he'd moved in the transfer market.
"That's why I have been working my tail off and thankfully we have got somebody we think will score goals," said Wilder.
"I have admired Tom Craddock for a long time. He comes with a pressure of having to score goals, but his record is a good one. Hopefully he can finish the chances we are undoubtedly creating."
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