According to The Mail On Sunday, the pair flew to the American city ten days ago in between Huq's filming of The Xtra Factor. It is claimed that they wanted to keep the ceremony private.
A source said: "Charlie didn't want a big, tacky celebrity wedding because he doesn't see him and Konnie as a celebrity couple.
"They are very much in love but when it came down to it, he wanted the wedding to be low-key. He is finding it hard to accept the level of interest in their relationship. If it was up to him, they would lead a totally private life, enjoying playing PlayStation games at home together and eating in.
"But it is different for Konnie. She is used to all the attention her job brings her and doesn't mind being in the public eye. Charlie gets frustrated when people are surprised that they are together.
"He doesn't understand why it is an issue. He knows that she is beautiful but he sees a different side of her that the public doesn't."
It was revealed in June that Huq and Brooker had got engaged after a secret nine-month relationship.