The 28-year-old actor is said to have reached out to the 'Bangerz singer', 21, in early December, reported Us magazine.
"The next day, they hung out. And they've been hooking up ever since," a source said.
Cyrus even invited Lutz on an overnight jaunt from Miami to the Bahamas on December 17.
"It doesn't hurt that he is Liam's pal. But they really enjoy each other's company," the source added.
Cyrus and ex-fiance Hemsworth split back in September after being together for three years.