The star married French restaurateur Jean-Bernard Fernandez-Versini earlier this month in a secret ceremony.
Cheryl reveal the news on Twitter a few days later, writing: I usually do not discuss my personal life but to stop the speculation I want to share my happy news... Jean-Bernard and I married on 7/7/14."
Appearing as a guest co-host on Radio 1's Greg James show on Thursday, she said that she would have been in favour of her second marriage remaining out of the spotlight.
"I would have actually kept it that way but unfortunately it was leaked," she told James, adding: "But I'm glad it's out there."
The couple were married on a beach in Mustique in front of just a handful of guests, after dating for three months.
She was previously married to footballer Ashley Cole but they divorced in 2010 after just four years.
The singer is on course for her fourth number one solo single with Crazy Stupid Love this weekend, and she explained that she had taken time away from the music business to allow her to "recharge".
Cheryl told James that a typical day for her during her downtime would see her "sit in my pyjamas watching TV, flicking through the channels".
The star - who returns to The X Factor nest month - had a party to celebrate her wedding earlier this week at smart London venue Library, with guests who included her Girls Aloud friends Nicola Roberts and Kimberley Walsh, as well as her mother Joan Callaghan.