Kidman and Cruise split shocked Hollywood
Cruise's publicist told Entertainment Tonight that the pair had been out on a few dates since he celebrated his 39th birthday.
It is the first high-profile relationship the star has had since his split from wife Nicole Kidman.
He is now said to be holidaying on the island of Fiji - with a woman not thought to be Cruz - just days after Kidman visited there at the same time as actor Russell Crowe.
Cruise and Cruz were first romantically linked after co-starring in the forthcoming movie Vanilla Sky.
Cruise's spokeswoman Pat Kingsley told Entertainment Tonight that they "had a few dates".
Co-stars
Cruz has previously been linked to her co-star in All the Pretty Horses, Matt Damon, who split from girlfriend Winona Rider during filming, and Nicholas Cage, with whom she appeared in Captain Corelli's Mandolin.
The Spanish actress has been vocal about the huge interest in her love life.
She told the Calgary Times: "It's such an absurd invasion of privacy, which is why actors lie so much about their private lives."
Cruise and Kidman, who have two children, ended their 10-year marriage in February and he has since filed for divorce.
The Australian actress is reported to have arrived at the Wakaya Club in Fiji with her two children Isabella and Connor and was later joined by Crowe, who was with a female companion.
According to divorce court file papers, Kidman begged Cruise not to end their marriage and later miscarried a baby she was carrying.