The couple, who started dating last year, got engaged New Year's Day, Playbill.com said. No other details were immediately reported.
"Thanks for all of the sweet congrats on our engagement," McDonald said in her online posting Tuesday. "We're super happy and excited."
UsMagazine.com said McDonald divorced bassist Peter Donovan in 2009 after nine years of marriage. The "Private Practice" actress and her ex have a 10-year-old daughter together. A four-time Tony Award-winner, McDonald can now be seen in the Broadway revival of "Porgy & Bess."
Swenson has two sons with his ex-wife Amy Westerby. He is one of the stars of the Broadway musical "Priscilla, Queen of the Desert."