When Cassius Clay beat Sonny Liston for the heavyweight title in Miami Beach in 1964, there were few public places where a black man, even a famous one, could go celebrate.

So Clay, who would soon become Muhammad Ali, took his friend and mentor Malcolm X to a celebration in Brownsville at his favorite hangout, the Hampton House Motel. It was the spot for Miami’s black movers and shakers during the last years of segregation, and the place where Martin Luther King Jr. held court with local civil rights leaders when he was in town.

Clay, who was living in Miami while training for the championship fight, usually ordered orange juice at the Hampton House’s famed jazz club. That night he had a generous bowl of ice cream to mark his big win.

Today, the place where Ali, King and celebrities like Sammy Davis Jr., Jackie Robinson, Sam Cooke and Nat King Cole slept, played, socialized or performed — along with thousands of more-ordinary people — is a roofless ruin, “just a frame being held up by some sticks,’’ in the words of Miami preservationist Enid Pinkney.

But that’s about to change.

After a decade of planning by Pinkney, other activists and Miami-Dade County officials, the Hampton House, among the most significant, still sort-of-standing places for a community whose iconic buildings have been largely wiped out, will be rebuilt to the hilt and reopened for a range of public uses, though not as a motel.

“We have waited a long time for this,’’ said a delighted Pinkney at a groundbreaking ceremony Thursday behind the Hampton House, 4200 NW 27th Ave.

The groundbreaking was symbolic, but a crew working for the contractor hired for the restoration, Link Construction Group, was already at work, cleaning up the site in preparation for the start of building within the next couple of weeks.

The historic motel’s two-story, 30,000-square-foot MiMo-style main building will be fully restored to its early ‘60s heyday, a $6 million endeavor funded mostly with proceeds from voter-approved county bonds. (The 12 apartment buildings behind it that were part of the motel were demolished and are being replaced by a privately developed affordable housing complex now under construction.)

The hotel reconstruction will put back what county project construction manager H. Patrick Brown called its “symbolic spaces’’ — several re-created guest rooms, including the “suite’’ that King is believed to have favored, which will be furnished in period stye and serve as a museum, as well as the café and restaurant space and the jazz club.

Preservationists rescued numerous items from the motel, including furniture, fixtures, railings and wall paneling that will be incorporated into the restored Hampton House, which the county purchased a decade ago to stave off its demolition.

One thing that won’t return: the swimming pool in which King was once photographed treading water in his swimsuit. The pool will be replaced by a shallow, decorative water feature.

Completion is scheduled for January 2015.

The nonprofit Historic Hampton House Community Trust will manage the building, which the organization hopes will be self-sustaining. It won’t operate as a motel, but Pinkney and her organization aim to find a restaurant operator, rent out the place for weddings and events, and lease office space in the building to local businesses.