The 27-year-old defender, who skippered the Blues to two US Premier League titles, has reportedly signed on a four-year deal with the Lightning and says he has fulfilled a lifelong dream of playing in England.
"This is dream come true for me, playing in the BritLeague," said Perry in his first press conference.
"Meeting the chairman, the manager and all my new team-mates for the first time was a big, big thrill."
As part of the deal, out of favour defender Jamie Hutchinson has been sent on loan to the Blues, who currently lead the US Premier League table.