Cahill won the FA Cup and European Cup within six months of his January 2012 arrival from Bolton but had to wait three more years to land a first English championship.
The Blues won their first Premier League title in five years after their Champions League last-16 elimination to Paris St Germain in March ended Jose Mourinho's quest for a third European Cup with a third club.
The England vice-captain now wants to win the Champions League once again.
"We want to make winning the Champions League more of a goal next season
We'd love to win it," Cahill told the London Evening Standard.
"We wanted to go as far as we can this season, but the league was vitally important for us too.
"A lot of the lads were talking at the start saying it was a long time since we'd won it (the Premier League)
We got a sense that it was the most important trophy to win in a way.
"We were disappointed to go out of the Champions League the way we did, even though we were unbeaten in the competition.
"It was a mad twist and that's what can happen at that level
But the aim is to do better in the competition next season and of course the squad is capable of doing that."
On finally adding the domestic title to his list of honours, which includes the 2013 Europa League and this season's Capital One Cup, Cahill added: "I have completed the set of medals but it's a fantastic achievement for the club
I have been here for three and a half years and managed to do it in such a short time, which is amazing.
"At the start of the season I wanted the title so badly, like the rest of the squad
I think everyone could tell that was the case during the campaign
To finally do it is fantastic."
Source : PA
Source: PA