The midfielder, 21, has signed a four-year £6million deal.
Shelvey said: “Leaving Liverpool was a very hard decision.
“But coming to Swansea, who play similar football which Brendan and managers before him installed, is an attraction.
“Brendan said he wouldn’t let me go to a club that wasn’t right for me. He said Swansea are perfect for the way I play.
“He couldn’t guarantee me the first-team football at Liverpool, and he said if I could get the game-time at Swansea then I should go.
“I need to come and play football and get myself to the status that I once had.”