Meg Ryan & John Mellencamp Quietly Dating

The pair spend time together on Martha's Vineyard and in N.Y.C. as the rocker announces his split from his wife

Photo: Ray Tamarra/Getty; INF

The new year brings new beginnings for Meg Ryan and John Mellencamp.

The pair have spent time together on Martha’s Vineyard and in New York City in recent days, enjoying a fresh romance just as Mellencamp has announced his separation from wife Elaine after 18 years of marriage.

A source close to Ryan, 49, says the actress and the rock star, 59, began dating about seven weeks ago, and that Mellencamp and his wife had been separated for some time before that.

The pair have been spotted having coffee at Espresso Love, one of Ryan’s favorite spots on the Vineyard, and grocery shopping at Gourmet Garage in New York’s SoHo neighborhood – where observers tell PEOPLE they seemed happy and at ease.

“She usually comes in by herself or with her daughter. I thought that was her husband because they seemed for comfortable and familiar with each other, just like an old married couple,” one observer says.

Mellencamp has been married three times and has five children, including two sons with Elaine.

Ryan has been married once, to actor Dennis Quaid. They divorced in 2001 after 10 years of marriage. They have a son, Jack Henry, who is 18. Ryan also has a daughter, Daisy True, 6, whom she adopted from China.

• Reporting by MARY S. PARK, JULIE JORDAN and LIZ McNEIL

For more on Ryan and Mellencamp’s new romance, pick up the new issue of PEOPLE, on newsstands Friday