Bulgari, which was bought in 2011 by French luxury giant LVMH, will put €1.5 million towards the refurbishment which will begin in 2015 and last two years, Rome's mayor Ignazio Marino said.
Italy's Prime Minister Matteo Renzi called this month for private investors to help restore and maintain the country's heritage monuments, after a series of wall collapses at the ancient ruins of Pompeii in southern Italy.
"Italy is a country of culture and so I challenge businessmen. What are you waiting for? If the private sector can keep the wall standing upright, why not allow it to?" he said.
The culture sector in Italy has suffered from harsh budget cuts and a deep recession and funds are expected to be cut further to €1.4 billion for 2014, from €1.5 billion a year earlier.
Many Baroque or Renaissance churches and Roman-era archaeological sites are kept permanently off limits to the public for lack of maintenance.
The government has already called on the private sector to help restore other UNESCO monuments: in Rome, luxury shoemaker Tod's is financing works at the Colosseum, while high-end fashion house Fendi is expected to refurbish the Trevi Fountain.
The Spanish Steps refurbishment will be "the special gift from Bulgari to its city" to mark the jeweller's 130th anniversary, the company's chief executive Jean-Christophe Babin told a press conference in Rome.
The 18th century Baroque-style stairway has 136 steps.