The final bill for the refurbishment of the 17th-century baroque mansion in Paris's historic Marais quarter now stands at €52 million ($71 million), or €22 million more than the original budget due to changes in the scope of the work.
The museum is scheduled to open to the public again in June, president of the gallery Anne Baldassari told news agency AFP, adding that a more than doubling of the space available would allow curators to really "do justice to the collection".
Although the museum has around 5,000 paintings drawings, sculptures, ceramics, photographs and documents, previously only a fraction could be displayed at any one time due to the limited space available.
The renovations will boost the exhibition space to 40,000 square feet (3,800 square metres).
There will also be a corresponding rise in the number of visitors that can be admitted at once from 380 to 650, and annual admission figures are expected to jump from 450,000 to 850,000.
Baldassari said that if all went to plan most of the works would be brought out of storage at the end of April and arranged for display during May. The museum closed in August 2009.
"It's been a revolution," she said.
"Everything is new, everything has a fresh coat of paint, everything has been renovated, everything works.
The museum will in future 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.
The Paris museum opened for the first time in 1985 with most of exhibits left to the French state on Picasso's death in 1973. Others were donated by his family including his widow Jacqueline.