"We have lovingly and carefully taken the time we have needed to arrive at our decision to separate," the couple said in a joint statement.
"We share an abundance of love and respect for one another and will continue to lead with our hearts from that place. We kindly request your compassion and respect for our privacy moving forward."
Hough, 31, and Laich, 36, married in 2017 after four years of dating.
They have not been social distancing together amid the coronavirus pandemic.
"They continue to spend time apart and are doing their own thing," a source told E! News earlier this month.
Another insider told UsMagazine.com the breakup was "a long time coming."
"They argued a lot and just had different viewpoints on important issues," the source said. "There's still a love there, but not in a romantic sense."