The midfielder, who has been capped once by the England senior side, moved to South Wales for a fee of £5 million last week, after finding first-team opportunities limited at Liverpool.
|20/1||Swansea are 20/1 with BetVictor to finish in the top six next season
"Less than two hours after I had agreed to sign, people were coming up to me in the local Sainsbury's in Swansea for autographs and pictures," said the 21-year-old.
"When I spoke to the Swansea chairman [Huw Jenkins], he said they had been tracking me from my Charlton days. I also heard of a link when Joe Allen was going to Liverpool, but that never happened.
"It raised its head again over the summer and I was following it in the papers every morning while on holiday until it happened for real."
The Swans will make their debut in the Europa League this season following last term’s Capital One Cup success, and Shelvey is relishing the opportunity to play on the European stage again.
"I've played European football for the last two seasons," he added.
"It's exciting for the fans and I'm sure the atmosphere will be buzzing at the Liberty for the night games.
"It will also give the players experience of going to different countries and facing different styles of play."