Academy graduate Carroll played a key role in the Magpies' promotion from the Championship last season and had continued to shine since being handed the club's number nine shirt during the summer.
Newcastle boss Alan Pardew had repeatedly stated that the player was not for sale but the club's owner Mike Ashley and managing director Derek Llambias have tried to bring a financial realism to the club during their time at the helm.
Former Magpies and England striker Alan Shearer told BBC Radio 5 live fans would be "angry and disappointed" that Carroll was sold, but the huge transfer fee would have been difficult to turn down.
"I'm staggered just like the rest of Newcastle fans," said Shearer.
"It's an incredible amount of money, you have to say that, for a guy who's scored - what is it? - 14 goals and had half a season in the Premier League, albeit having done very well and the potential is there.
"He's a very young guy, he's been in trouble once or twice before and that would be the major concern."
"It's all right selling your best player, but not getting anyone in to replace him is staggering.
"People are saying that Liverpool have sold Torres, but they have got two guys in [Luis Suarez and Carroll] for over £50m to replace him. I just hope Newcastle invest some of the £35m in new players at the end of the season.
"He is a huge loss, he has carried Newcastle at times this season. There are not many players like him."
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