"Yes, we are excited to confirm that they are engaged!" says the rep.
The couple began dating in May, after being introduced by friends. Ever since, they have been spotted getting cozy across the U.S. and overseas – even celebrating her 30th birthday together in Italy.
Simpson recently told PEOPLE she and Johnson, 31, were planning to spend Thanksgiving together.
"We're all gonna be in New York," said the entertainer and fashion designer. "I'm gonna be on a [Macy's parade] float. It's not always the best way to spend a Thanksgiving, but it's a great way to celebrate. So, maybe I'll just have all families on the float."
Explaining how well their relationship was working, Simpson told PEOPLE last month, "This is just normal, thank God. He's very, very supportive. [I] couldn't ask for a better man in my life right now."
Asked if Johnson were the one, she replied: "I never go to that because I already went there, so, I'm not gonna jinx my own self. He's the one for me right now! I'm very happy, I'm in a great place and if right now could last forever, I'd take it."
As for Johnson, who's played for the San Francisco 49ers and the New Orleans Saints, the 6' 3" Needham, Mass., native has excelled at sports since he was a kid. At 13, he hit a hole in one on the golf course, and he broke 11 school records while playing wide receiver for Yale University. He's also a former academic All-American.
Spreading the LoveAlso chiming in this past week, Simpson's brother-in-law, Pete Wentz, told PEOPLE about Johnson: "He's a really smart guy, and Jessica really loves him. I think that's the most important thing, seeing her happy,"
Spreading the love herself, only a few days ago Simpson expressed her delight over the engagement of her ex-husband, Nick Lachey to Vanessa Minnillo, saying, "I couldn't be more happy for Nick."
Simpson and Lachey split in 2005, after three years of marriage.
Reporting by K.C. BAKER and LESLEY MESSER