The 21-year-old has put pen to paper on a four-year contract at the Liberty Stadium.
Swansea chairman Huw Jenkins has spoken of the need to increase the quota of homegrown players at the Liberty Stadium and Shelvey fits the bill.
"We have got to make sure that the make-up of our squad is right," said Jenkins.
"And obviously part of that is making sure that we have so many British players in there. We have got to do that - there is no choice because they are the rules."