Wheater, 23, goes straight into the squad for the home game against Chelsea on Monday after signing a three-and-a-half-year deal.
Coyle said: "We would like to add to our squad again. We are in the market but a few boxes need to be ticked for that to come to fruition. David Wheater is an exciting signing and shows again if we are going to spend money we are going to invest it in young players."
Coyle is tipping Wheater to win back his place in the England squad - he was called up in 2008.
"I am absolutely delighted to bring a quality player to the club and at young player at that at 23, " said the Bolton boss.
"He has already played in tremendous fashion in the Premier League and been involved in some England squads. We want to get him back to that level. To do that he was to do well for Bolton. David has a number of strengths. He is dominant in the air and comfortable on the ball. He can pass the ball well and is a good reader of the game."
Wheater has already finished second best to Coyle - at table tennis.
They had a game at the club's Euxton training complex as he waited for the results of his medical.
Wheater said: "One of the first things the manager mentioned to me was how good he is at table tennis and I got slaughtered. So I need to improve. Hopefully he can improve me as a footballer as well. I was ready for the move. I was at Middlesbrough a long time and I needed to make that step up.
"The chance to play in the Premier League was too good to turn down, especially with the type of manager at Bolton and the players here."