The couple, who met on The X Factor, married in the chapel of Mount Stuart House on Bute, where fashion designer Stella McCartney held her wedding in 2003.
JB told Hello! Magazine: "Chloe and I are both traditional in our views and our values. For me, marriage is the union of a man and a woman before God, so it meant a lot to us to have a proper church service with hymns."
He also revealed the couple's traditional values went as far as living apart before the wedding, saying: "Like I say, we're traditional, and to us that's all part of this exciting new chapter in our lives. For me, it's a big thing.
"When you get married, it's not just you any more, it's the two of you and I'm looking forward to reflecting that in our home.
"Today has been the best day of our lives and for now, we're happy to spend some time enjoying what we have and getting used to being husband and wife. It feels so good to finally be able to say that."
JB said seeing Ms Tangney coming down the aisle calmed any nerves he had: "I was desperate to see Chloe. I'd missed her.
"I know it sounds cheesy, but it was perfect."