The 50-year-old actress, who split from Cydney Bernard in 2008 after 20 years together, is now in a relationship with Hedison, reported E! online.
"It is pretty serious. They are totally in love," a source said.
Alexandra dated Ellen for three years before the couple split in 2004 and the chat show host went on to marry Portia de Rossi.
Earlier this year Foster publicly acknowledged her sexuality for the first time as she accepted the Cecil B DeMille Award - which is given in recognition of outstanding achievement - at the Golden Globe Awards.
"A big coming out speech tonight... I already did my coming out about a thousand years ago, back in the stone age. In those very quaint days when a fragile young girl would open up to trusted friends, and family, co-workers and then gradually, proudly, to everyone who knew her.
"To everyone she actually met. But now, apparently I'm told, that every celebrity is expected to give the details of their private life with a press conference, a fragrance and a prime time reality show ... I'm sorry, that's just not me and it never will be," she had said.
