Adele confirmed the news at a concert here over the weekend, reports aceshowbiz.com.
The couple has been together since 2011 and they have a four-year-old son named Angelo.
"I was trying to remember how it was I felt at the beginning of the relationship that inspired that record," Adele told the crowd while sharing the story behind her hit song "Someone like you".
She added: "Because as bad as a break-up can be and as bitter and horrible and messy as it can be, that feeling when you first fall for someone is the best feeling on earth, and I am addicted to that feeling. Obviously, I can't go through with those feelings because I'm married now."
She offered no other details about her marriage, but she reportedly exchanged vows with Konecki in a low-key ceremony after Christmas in front of family and close friends at her Los Angeles mansion. She even called Konecki her "husband" at Grammys last month.