"Can you see anything?" whispered Lord Carnarvon as, with the light of a candle, Howard Carter peered for the first time into the tomb of Tutankhamun. "Yes, wonderful things," came the famous reply. Those wonderful things came to light on 26 November 1922, sparking a popular and enduring fascination around the world with all things ancient, mummified and Egyptian.

The Ashmolean, Britain's oldest public museum (founded in 1683), will this Saturday open the doors of six newly refurbished galleries devoted to its collection of some 40,000 Ancient Egyptian and Nubian antiquities - a collection of outstanding quality.

Spanning the Nile's cultural history, from its prehistoric roots to the days of Egypt under Roman rule, the objects on display here are hugely important from a historical point of view. Mesmerising, too. The new galleries mark the completion of a second phase of the £66m renovation and transformation of the Ashmolean by its director, Christopher Brown and his architect, Rick Mather. The first opened to critical acclaim in 2009.

Collected by the museum over 300 years from more than 100 archaeological sites in Egypt and what is Sudan today, many of the newly restored objects have been in store since the second world war. Highlights include the shrine of Taharqa from the Temple of Kawa [c680BC], the only complete freestanding pharaonic building in Britain, statues of the fertility god, Min, carved around 3300BC and a wall painting in a remarkably naturalistic style of the daughters of Nefertiti and Akhenaten

And there is truly something for every taste. Mummies, of course, along with canopic jars, a gloriously detailed 3,750-year-old model funerary boat still with its canvas sail, a green glass fish, a bunch of multicoloured glass grapes, a putty hippopotamus, a mummified ibis and haunting portraits of newly dead young Egyptians staring out at us, disconcertingly, like young rock stars and fashion models and as if they had never really left this world.

Each of the six galleries has a different theme and a character of its own, beginning with Egypt at Its Origins and ending with Egypt Meets Greece and Rome. Pre-dynastic sculptures occupy the tall and magnificently daylit Ruskin Gallery previously occupied by the museum's shop, although in the late 19th century it was home to John Ruskin's School of Drawing and Fine Art. Ruskin was the university's first Slade Professor of Fine Art. The shrine of Taharqa, shipped in crates from Sudan to England in 1936, broods at the centre of the renovated Griffith Gallery under a glazed vault designed by Mather that, in the absence of razor-sharp Egyptian sunshine, serves to highlight the incised carvings around the 2,600-year-old structure.

Smaller objects are gathered in stone floor-to-plaster ceiling display cases set into gallery walls. These are finished in warm colours, red predominating, and are combined with intelligent captions, clear graphics and thoughtful lighting.

"The Egyptian galleries used to be a series of little dark rooms," says Mather, "finishing with a dead end that you almost had to feel your way out of. But they were full of the most amazing objects - the collection rivals the Cairo Museum in some areas - so we've made them into a route that visitors can find their way around easily and naturally, without a map, but with the feeling that they're finding things by serendipity. There are glimpses through to other galleries, each leading you on gently to the next. And there are no dead ends."

The story of Ancient Egyptian archaeology is brought up to date with a representation made in glass from 2,500 CT scans of the body of a two-year-old mummified child who died around 100AD. The artwork, by the sculptor Angela Palmer, allows visitors to see the form of the child inside the unwrapped flax linen mummy. The scans were made by radiologists at the John Radcliffe Hospital, Oxford. They reveal that the boy probably died of pneumonia.

The £5.2m Egyptian and Nubian galleries, funded largely by the Linbury Trust, were granted planning permission last November, and have been driven along quickly by a team spearheaded by the museum's Liam McNamara, assistant keeper, Ancient Egypt and Sudan - an expert in late pre-dynastic and early dynastic Egyptian archaeology. Here, architects and curators have created a special place where "wonderful things" from along the Nile can be seen and experienced as if for the first time.

Jonathan Glancey