"I will say the same thing I always say: I wish her the very best," he told UsMagazine.com Monday during a conference call for his NBC singing show The Sing-Off (season 2 kicks off Dec. 6).
As for his own engagement, he told Us he and Minnillo, 30, are "still basking in the glow" of the news and "are enjoying that. I'm sure we'll get on the other planning shortly. We are now just enjoying this experience."
He told Us it is "very exciting" to see "what the future brings to us."
Asked why it took him so long to propose, he said, "All things have their appropriate time, so thank you."
Simpson and Lachey famously wed in 2002 (he got choked up singing "My Everything," a 98 Degrees song he wrote for her).
By 2005, the two announced they were splitting. "This is the mutual decision of two people with an enormous amount of respect and admiration for each other," they said in a statement.
Asked how she felt about Lachey's recent engagement, Simpson told radio host Ryan Seacrest last week: "Our relationship was over a really long time ago, and it would be nice if everyone could move on with us and really just celebrate the love between him and Vanessa. I do, and I really wish them nothing but the best."