Coyle revealed more than a fortnight ago that a fee - believed to be around ?7million - for the England defender had been agreed between the two clubs, but there has still not been any official announcement to confirm the deal is done.
Cahill had his medical at Chelsea before watching their 1-0 win over Sunderland from the stands at Stamford Bridge on Saturday, and asked this morning for an update on the situation, Coyle said: "My understanding is that everything is agreed."
He added: "The clubs agreed (a fee) a number of weeks ago, the player, his representative and Chelsea have agreed, and I think he sailed through the medical as we all would expect.
"For me, between today and tomorrow morning, it is just a matter of the contracts being exchanged between the relevant parties to conclude the deal.
"As far as I am concerned, Gary is joining Chelsea."