The 21-year-old travelled to Swansea on Wednesday morning and agreed terms on a four-year contract, before successfully completing a medical examination.
"Everybody at Liverpool FC would like to wish Jonjo all the best for the future."
Shelvey joined Liverpool from Charlton Athletic for a fee of £1.7m in May 2010 and went on to make 69 appearances for the five-time European champions, scoring seven goals.
He made his England debut in a 5-0 FIFA World Cup™ qualifying win over San Marino last October.
The cost of Shelvey's move to Swansea could rise to £6m, depending on additional performance-related bonus payments.
Writing on his Twitter account, the midfielder said: "Just want to to say thank you to every one of the Liverpool fans for there (sic) support! They were first class. And will be truly missed.. Will miss The city very much.. And the club!
"Owe a lot to everyone there! Thank you. Time to start a new chapter in life in Wales. Thank you."