Wheater's fee, which could eventually amount to £3million, will help to finance his rebuilding work, while his removal from the wage bill will give the Teessiders further leeway.
But Mowbray told the club's official website, www.mfc.co.uk: "I'm disappointed for the club.
"He's been a very important player for us, but we do need to put ourselves back on a sound financial footing to build and push forward from.
"David's contractual situation was the main reason why he's gone. We endeavoured to see if he would put pen to paper on a new deal, but that wasn't going to come to fruition.
"We have got some money back in and we wish David well."