Jessica Simpson and Nick Lachey have resolved the splitting of their assets, according to legal documents obtained by PEOPLE.

It officially brings their divorce to a complete close; the couple were legally free to marry others last June.

Details of their settlement are undisclosed.

Simpson, 26, and Lachey, 33, were married in 2002, and starred together in the MTV reality series Newlyweds: Nick and Jessica. They separated in June 2006, and filed for divorce that December.

Simpson, who decamped to her own Beverly Hills mansion, has kept busy with music and movie work. She has spent the past few months shooting her latest film, Blonde Ambition, in Shreveport, La.

Lachey, who is scheduled to host a party at Pure Nightclub in Las Vegas on Saturday night, spent his time since his marital breakup renovating a Bel Air bachelor pad and amping up his music career with the gold-selling album What's Left of Me and a nationwide tour.

He's also found love again with MTV's TRL Vanessa Minnillo, 26, whom he's been dating for eight months.

"The first few months were hard," a pal of Lachey's told PEOPLE in November. "But Nick finally realized he was in a better place."