Cahill has become Villas-Boas' first recruit of the January transfer window, with the 26-year-old England defender's move from the Reebok Stadium to Stamford Bridge finally being confirmed on Monday.
"I think there is - as with any player - room for expansion and improvement. He has now gone to an elite club who have aspirations of winning every competition they enter," said Coyle.
"I think that will push him on to another level, and he is competing with world-class players now for his position in the team.
"He is working with a fantastic manager, who I know well and is someone who wants to build a club at Chelsea.
"I think Gary will be a huge part of that."