"He's been sweeping her off her feet and courting her like a proper gentleman," a source told People of 45-year-old Jose, who is the president of Televisa, the largest media company in Latin America.
The couple made their first red carpet appearance together on Friday evening, when Jose escorted Eva, 38, to the Museo Jumex Opening dinner at Case De La Bola in Mexico City.
They caused quite a stir as they arrived for the event, happily posing for photographs together before heading inside.
Eva looked beautiful in a fitted monochrome cocktail dress, and her handsome parter proudly wrapped his arm around her waist as they smiled for the cameras.
Last month, the couple were spotted dining together at New York's Serafina restaurant. At the time, it was claimed that Eva had reconciled with former boyfriend Eduardo Cruz for the dinner date — but it was later revealed that her companion was Jose.
Eva's former boyfriends Ernesto Arguello and Eduardo Cruz
"They were very cute together, holding hands and giving each other little kisses," a witness told E!.
"They were adorable. Eva was in a great mood, huge smile on her face and very kind to the staff."
A source told People, "She's very happy and he's crazy about her."
Eva has been single since splitting from Ernesto Arguello in August after four months of dating. She ended her romance with Eduardo, Penelope Cruz's younger brother, back in March.