French President Francois Hollande said at a ceremony the museum was "one of the most beautiful in the world and one of the most moving because it brings together the considerable and prolific work of the best-known artist of the 20th century".
The ceremony, though, did little to hide the rancour surrounding the project, which featured the sacking of its director, a blast of criticism from the artist's son, lengthy delays and a huge budget overrun.
The museum — housed in a 17th-century mansion in Paris's trendy Marais quarter — has been extensively modernised and enlarged to more than twice its previous size.
But the project ran 22 million euros over budget due to an increase in the scope of the works, and a rift developed between Picasso's son Claude and the French government.
The gallery, which first opened in 1985, boasts one of the world's most extensive collections of Picasso's work with 5,000 paintings, drawings, sculptures, ceramics, photographs and documents.
The Spanish artist spent most of his life in France and the majority of the exhibits were left to the French state on his death in 1973.
Others were donated by his family, including his widow Jacqueline.
Hollande also used the opening to defend a US contemporary artist, Paul McCarthy, who had a controversial inflatable work in Paris' chic Place Vendome — meant to be an abstract Christmas tree, but viewed by many as an overscale green sex toy — was vandalised last week, leading to its removal.
The president condemned "the act of stupidity which leads to an artist being attacked or his work being destroyed".
"The talent of a nation can be measured by the importance it accords to artists," Hollande added.
According to the Picasso Museum's new director, Laurent Le Bon, the expansion — which has boosted the exhibition space to 3,800 square metres (41,000 square feet) — will allow it to display far more of its collection, only a fraction of which was previously displayed due to lack of space.
Le Bon told AFP the beauty of the renovation was that "everything has changed and nothing has changed".
"You still have the basic structure of the building… but at the same time everything has been redone," he said.
"One can move around much more easily than before, one has a freedom which goes well with the spirit and the works of Picasso."
As part of the refit, offices have been turned into exhibition areas, former stables transformed into a huge reception hall and the basement excavated.
New minimalist exhibition spaces are characterised by grey terrazzo, bare stone and whitewashed walls.
But the sacking of the museum's previous director Anne Baldassari in May 2014, just months before the re-opening, has cast a shadow over the project.
The director, who had been at the helm for nine years and at the museum for over two decades, was summarily sacked by France's then culture minister, Aurelie Filippetti, following a staff rebellion and accusations of authoritarian management.
Her dismissal prompted Claude Picasso, who supported Baldassari, to accuse the French government of failing to value his father's work and of dragging its feet over the re-opening.
Baldassari "is the scientific authority who has been responsible for the growth of the museum for many years," Picasso told the newspaper Le Figaro at the time, adding that he would regard any replacement who thought they could take her place as an "impostor".
In future, the museum is expected to hold one major exhibition each year.
The first in mid-2015 in collaboration with New York's Museum of Modern Art will take Picasso's sculpture as its theme.