The midfielder, who has been capped once by the England senior side, called time on his career at Anfield to make the switch to South Wales for a fee of £5 million after falling out of the Northern Irishman's plans on Merseyside.
Speaking to reporters, Shelvey acknowledged it had been a difficult decision to leave Liverpool but on the advice of Rodgers, chose to move to Swansea in search of more opportunities for first-team football.
|100/1||Swansea are 100/1 with Bet365 to finish in the top four next season
"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."
After moving to Liverpool as a highly-rated youngster from Charlton three seasons ago, Shelvey made 70 appearances in all competitions for the Reds, scoring seven goals.
However, despite beginning the 2012-13 season as a regular, the January signing of Philippe Coutinho pushed Shelvey down the midfield pecking order and hastened his summer departure.
"[Rodgers] 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."
Shelvey is already Swansea's fifth signing of what is proving to be a busy summer of transfer business at the Liberty Stadium, as Michael Laudrup bolsters his squad ahead of their maiden campaign in the Europa League following last season's Capital One Cup success.