What do a 15th-century sculpture and an Ikea table have in common? In the case of Luca della Robbia’s “The Visitation’’: Both require assembly.

“The Visitation’’ arrived at the Museum of Fine Arts in four pieces — two disembodied ceramic heads and bodies. Late last month MFA staff and Italian conservators undertook the painstaking process of reassembling a glazed terra cotta statue that’s about 570 years old.

“It is now considered Luca Della Robbia’s masterpiece in this medium that he invented,’’ exhibition curator Marietta Cambareri said. It’s the centerpiece of the museum’s exhibition of della Robbia sculpture, which opens Aug. 9.

Della Robbia designed the sculpture to break down into four parts — as he did with much of his work. Sometimes, della Robbia and his family even left instructions for how things ought to be pieced together, as his sculptor nephew Andrea did on his own “Prudence,’’ a roundel loaned by the Metropolitan Museum of Art in New York. It came in 15 pieces and was assembled based on numbers inside the seams.

Luca della Robbia likely designed things in pieces for two reasons, Cambareri said. One was that Renaissance-era kilns may not have been very large, so firing a work in pieces was easier. The other was so his sculpture could travel easily.

“It would have traveled in carts, pulled by oxen,’’ Italian conservator Laura Speranza said.

Now “The Visitation’’ travels a bit more securely. It came from a church in Pistoia, Italy, and had a long layover in a Florentine conservation lab. There it got a serious makeover. Speranza said that the sculpture was yellow from the black smoke of church candles, so they spent about four months restoring its white surface. Then it was packed onto an airplane in four crates and flown to Boston.

There are no instructions on “The Visitation,’’ because its four pieces fit together in an obvious way. When it’s in one piece, the statue depicts a scene from the Gospel of Luke. Mary visits her older cousin Elizabeth while they are both miraculously pregnant — Mary with Jesus and Elizabeth with John the Baptist. When they meet, the baby jumps in Elizabeth’s womb, as if he recognizes Jesus before he is born.

Last month, though, Mary’s head was still separate from her lower body. The statue was unpacked and the four parts sat, disembodied, on pedestals while MFA head of objects conservation Pamela Hatchfield and Speranza inspected it for any possible chips or cracks that might have occurred on the trip.

“There are concerns, of course, because any time you move a work of art you’re putting a stress on it,’’ Cambareri said. “But it actually travels quite well, because the four pieces are quite compact.’’

Cambareri was instrumental in allaying concerns about travel in the first place. Securing the piece, which has never left Italy before, involved well over three years of work. She visited Florence and Pistoia five times. Because the statue was originally in a church, she had to consult religious authorities in Italy.

“The diocese of Pistoia answers to the Vatican, so people jokingly said to me, ‘You’re going to need the permission of the parish priest, the bishop of Pistoia, and the pope,’’ she said. Ultimately, that proved an exaggeration, but barely. Cambereri got permission from the parish priest, the bishop, a government representative, and a conservator who deemed it safe to travel.

After the conservators decided that no chipping had occurred, everyone left the gallery but eight people. Handlers carefully lifted Elizabeth’s head onto her body. The pieces rested together on top of a cushion that conservators in the Florentine lab had created.

“This avoids the direct contact between the two sections,’’ Esperanza said. “Before our restoration, the upper part touches only four of five points so it was very dangerous for the health of the parts.’’

So the conservators used a solution that della Robbia would never have envisioned: a 3-D printer. They used 3-D scanning technology to scan the statue’s shape and a 3-D printer to create pieces that would allow the top halves to rest more safely on the bottom halves.

Elizabeth’s head did rest safely, after it was moved. At that point, the statue was placed on its platform and looked like a puzzle that’s missing one piece — Mary’s head.

“You can see that when it was cast, Mary’s hand was part of the upper body of Elizabeth, and that Elizabeth’s hand is coming around Mary,’’ Cambareri said. “So even in the way it’s made, it’s got this unbelievable emotional quality.’’

Finally, Mary’s head was lifted on, and the pieces interlocked. Mary and Elizabeth touched. Against a white background, the glazed ceramic figures gleamed all white — except for their eyes, which are light blue. From one side, it’s possible to see where Elizabeth’s top half meets the bottom. From the other side, the folds of the dresses mask all the seams, and it appears to be one single piece.

But it wasn’t quite done. Hatchfield and others wedged foam padding into the arm joint where the pieces touch. Then they pulled some padding out, and stuffed some back in.

The fiddling was related to the statues’ relative heights. “The figures shrunk and moved a little bit in the firing,’’ Hatchfield said, “So they’re not perfectly in register with each other.’’

But then they were. After testing the solidity of the arms by shaking them a bit, and stepping back, Hatchfield declared that they were done, after about five hours of assembly. Everyone in the gallery clapped: “The Visitation’’ was finally really here.

Sophie Haigney can be reached at sophie.haigney@globe.com. Follow her on Twitter at @SophieHaigney.