The 20-year-old spent 18 months on loan with the Scottish champions from Manchester City between January 2016 and the end of last season and after a long drawn-out saga this summer, eventually returned to Parkhead on a season-long loan.
Former Liverpool boss Rodgers was instrumental in making that deal happen and the young winger is keen to repay the faith shown in him.
Speaking to the club website Roberts said: 'The manager knows what I bring, he knows the type of player I am and that's why he's brought me to the club.
'He puts a lot of trust in me at such a young age and I strive to repay that. He's been good ever since he came here and I can only get better for him.
'I haven't set myself any specific targets. I just want to keep improving as a player and to win as many games as I can, and stages like the Champions League play a big part in that.'