"I am extremely, extremely happy for him," the singer-actress, 30, told Ryan Seacrest on his KIIS-FM radio show Thursday. "I couldn't be more happy for Nick."
Simpson dismissed rumors that she wasn't thrilled to hear that Lachey, 37, got engaged this month to girlfriend Vanessa Minnillo, 30.
"I don't know where all those rumors came from," she said. "My mom actually called me and told me that everybody was saying that I was 'saddened.' And I was just in complete shock."
She added: "You know, our relationship was over a really long time ago, so it would be nice if everybody could move on with us and really just celebrate the love between him and Vanessa. I do, and I wish them nothing but the best."
Simpson and Lachey split in 2005 after three years of marriage. Lachey and Minnillo began dating the following year.