Chelsea were not in continental competition last term after the previous year's implosion, when Jose Mourinho was sacked for a second time and they went on to finish 10th in the Premier League.
It was the first time in 20 years that Chelsea were not involved in Europe and they had featured in every Champions League group stage since 2003-04.
Cahill, a European Cup winner with the Blues in 2012, said: "We feel we're back where we belong, which is among some of the very best teams."
Head coach Antonio Conte has Champions League pedigree as a player, reaching four finals, winning once.
He took Juventus to the quarter-finals once as boss and the Bianconeri have thrived in the competition since he left to take charge of Italy.
He wants to make his mark with Chelsea, but knows it will take time.
"In the Champions League we are starting a path and it will be very important to start building something important," he added.
"To win a competition, you need to work very hard, to improve over years and to grow step by step and to become like Real Madrid or Bayern Munich..
Juventus are the same now.
"You don't create a big strong team easily."
Conte plans to rotate his players for the second of seven games in September, but defender Cahill is desperate to play, having served a three-match ban following his dismissal in the season-opener against Burnley.
The club captain added: "I feel like my season's just starting
I'm itching to play."
Midfielder Danny Drinkwater (calf) is unavailable with the full extent of his injury sustained in training on Sunday still to be determined.
Playmaker Eden Hazard is likely to continue as a substitute after only recently returning from a broken ankle, but Conte is likely to switch personnel due to the domestic challenges which await.
The Italian said: "You are never relaxed in England, because you have to play a tough league and also in the FA Cup and Carabao Cup.
"In my past, sometimes before a Champions League game you rested
In England it's not easy to do this."
Sunday's league clash with Arsenal follows before a midweek Carabao Cup tie with Nottingham Forest for the Blues, who won the Premier League in Conte's first season as boss.
Conte knows whenever he chooses to rotate there is a "risk".
He added: "It's normal when you have to play seven games in 21 days to rotate my players
I'm very calm about this because I trust my players."
Source : PA