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Revealing the news, Simpson's representative tells People.com, "Yes, we are excited to confirm that they are engaged!"
Simpson and Johnson began dating in May (10) while he was estranged from his first wife, stylist Keri Johnson; their divorce was finalized last month (Oct10).
The singer recently opened up about their relationship, gushing to the website, "This is just normal, thank God. He's very, very supportive. (I) couldn't ask for a better man in my life right now."
Simpson and Lachey, who appeared together on MTV reality show Newlyweds, divorced in 2006 after three years of marriage.