Rachel announced the news with a picture of them she posted on Instagram on Monday, along with the caption: “Introducing the new Mr and Mrs Kovalev.”
According to Press Association, records from Clark County, the area of Nevada which includes Las Vegas, show the pair were wed on Friday.
Pasha’s former Strictly colleagues were among the first to offer their congratulations, with Katya Jones and Janette Manrara commenting with well wishes on the photo.
Rachel and Pasha are currently expecting their first child together, announcing their happy news back in May.
The pair met when they were partnered on Strictly Come Dancing in 2013, becoming the fifth couple to be eliminated.
Shortly after the series, Rachel announced she had split from her husband Jamie Gilbert after 16 months of marriage, and it was later revealed she and Pasha had embarked on a romance.
Rachel and Pasha are the second Strictly couple to tie the knot, after former Coronation Street actor Jimi Mistry married Flavia Cacaca three years after being paired up on the show in 2010.
Earlier this year, Pasha announced he was leaving Strictly after eight years as a professional dancer.