The Welshman signed a two-and-a-half year deal at Montgomery Waters Meadow after ending his five-month spell with National League Wrexham – his first senior job in management.
Ricketts, 37, retired from playing in 2016 and coached in former club Wolves' academy before taking the Wrexham hotseat in the summer.
He went into the academy route under the advice of former Liverpool boss Rodgers after an educational trip to shadow the Celtic Park boss.
"I think everyone has to start somewhere in football. I easily could've started at this level," said Ricketts, who led Wrexham to fourth in the National League.
"As it happened I went down academy football, after I finished playing I spent time with Brendan Rodgers at Celtic or others I knew or played under or I respect.
"Brendan gave me some advice, he said go and work with the youth team for a while, make your mistakes there.
"When you're ready come back into first-team football.
"I went into Wolves for the year at the academy and then the opportunity came to go to Wrexham for first-team football.
"I've done well enough to have the opportunity to come to Shrewsbury."
Ricketts is a close friend and former colleague of former Town midfielder Edwards, who he played with for Wales and Wolves.
Edwards, now at Reading, was one of the reasons Ricketts always had an eye on Shrewsbury, alongside the club's potential.
He added: "I speak to Dave an awful lot, team-mates for many years with Wales and Wolves.
"Dave is a good friend, we spoke at length and that's why for the last four or five years I've looked at Shrewsbury and thought what a really good club with really good facilities and well run.
"It's a really good platform for any manager to come in. I'm hugely fortunate and honoured to be here."