Coyle revealed more than a fortnight ago that a fee for Cahill - believed to be around £7million - had been agreed with Chelsea, and the transfer has finally gone through.
Cahill had his medical at Chelsea and watched their 1-0 win over Sunderland from the stands at Stamford Bridge on Saturday.
With Cahill departing, Coyle is optimistic it will not be long before the signing of Ream from New York Red Bulls is sealed.
"He is a player that we would love to bring to the football club and hopefully in the next few days that can come to fruition," Coyle said.
Meanwhile, the Scot has played down talk that he looking to make a move for Tottenham forward Giovani Dos Santos.
"We haven't been speaking to the lad," Coyle said. "There are fantastic young players out there in the Premier League and he is certainly one of them, but it is just speculation.
"There is no doubt that he is a top player, but there are many top players out there."