Cahill attended Saturday's game against Sunderland at Stamford Bridge, which the Blues won 1-0 thanks to Frank Lampard's goal, and is expected to be confirmed as a Chelsea player in the next 24 hours.
He travelled to London on Friday to undergo a medical after lengthy talks finally yielded a resolution, and Villas-Boas is looking forward to working with the England international.
The Portuguese manager believes Cahill possesses all the attributes needed to be a success with the Blues.
"He adds to a very solid back four that we have," Villas-Boas told Sky Sports.
"Gary is a player of tremendous technical qualities for a central defender, which is what we like, because of our possession when we build up from the back.
"He has good stamina and a good sense of anticipation, which were the characteristics we were looking for and we managed to get an England international."
However, the Portuguese has ruled out any more high-profile signings in the January transfer window, telling Chelseafc.com," In the January transfer market you can overpay and you don't have maybe the talent that you want available and you end up maybe choosing players that were not your first option regarding your future project. That's why apart from Cahill we don't expect anything else."
Contrary to previous reports, Villas-Boas claimed he doesn't believe Chelsea are out of the title race, saying, "We never went past the 13-point margin I set out.
"This is the nature of the Premier League. I would be the first to assume it when I see the margin is unobtainable and I don't feel it is unobtainable now - and I think it's good Tottenham are up on the run as well because more points will be dropped.
"What the other teams see in our run of results is inconsistency which is a fact and that's what we are trying to set right because it is not to our levels. This has been our cancer this season, that we are up and down in terms of results."
Chelsea got a much-need win over Sunderland on Saturday, thanks to a Frank Lampard tap-in after Fernando Torres' thunderous overhead kick had cannoned off the crossbar.