The England international has completed a £6million move to the Liberty Stadium after being informed that he could not be guaranteed regular first team football at Anfield.
Shelvey is hoping to use the switch as a catalyst in his career, with the 21-year-old looking forward to playing in a side which suits his game.
Rodgers played a leading role in making the Swans the eye-catching outfit they are today and he helped to persuade Shelvey that he can blossom in south Wales and add to the solitary senior England cap he earned in October 2012.
"Leaving Liverpool was a very hard decision," said Shelvey, who was snapped up by the Reds from Charlton Athletic in May 2010.
"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 could get 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."