Spanish banking giant BBVA is switching its 110,000 staff to use Google's range of enterprise software.
The deal is the biggest that the search giant has signed with one company for its cloud-computing services, where software is offered as a service via the internet.
The bank told the BBC it would use Google's tools only for internal communication.
But the deal can be seen as a breakthrough in corporate adoption.
Banking - with its high security needs and strict regulations - was always considered to be one of the last industries to accept cloud-computing.
BBVA's director of innovation, Carmen Herranz, stressed that all customer data and other key banking systems would "stay in our own data centres" and be completely separate from the cloud solution.
The bank would use Google applications like email, calendar, docs, chat, video conferencing and other collaboration tools to "achieve a cultural change" and get "the whole company working together" across the 26 countries where BBVA is based.
Ms Herranz said the project - with roll-out across all employees to be complete by the end of the year - was not about saving cost.
"The main goal is to promote innovation and making decisions and increase productivity. We are in a challenging market and need to make faster and more accurate decisions... and eliminate duplication," Ms Herranz told the BBC.
Also driving the change was the increasing mobility of the bank's workforce. A lot of the bank's computing needs had moved to smartphones, tablets, laptops and computers at home, she said.
Jose Olalla, chief information officer at BBVA, said because workers now had "access [to] the information they need at any time from any internet-connected device, anywhere in the world, [they] will be able to be more flexible and mobile".
BBVA is one of Spain's largest banks.
It is also the largest provider of financial services in Mexico, and has a large presence in the south of the United States.
'Largest ever deal'
Traditionally, companies have done all their computing on their own premises, to keep their data secure and to stay in control.
However, most enterprises leave some 80% of their computing power idle, and find themselves spending more than two thirds of their information technology budget on maintenance and software upgrades.
Cloud computing tends to be much more efficient, with firms like Amazon Web Services running their servers at more than 90% of capacity. That cuts cost and also helps the environment.
The man in charge of Google Enterprise apps in Europe, Sebastien Marotte, said that his corporate customers on average achieved cost savings of between 50% and 70%.
But the deal with BBVA, argues Mr Marotte, is important not only "because it is the largest ever agreement we have signed with an organisation, it is important because it is a very large financial company, it shows that now even banks are moving to the cloud".
BBVA's data would not reside on dedicated servers - a solution known as private cloud - but would sit distributed across the public cloud of Google's data centres. Both Mr Marotte and Ms Herranz stressed this would meet the demands of banking regulators and data protection officials, and be as secure as any solution on the bank's premises.
A bigger worry will be whether BBVA's computer network will be able to cope with the sharp rise in network traffic that cloud-computing solutions demand.
A pilot with 7,000 staff had not seen any issues, but the bank would closely monitor for any increases in network load. "Our biggest worry is around video conferencing," said Ms Herranz.
Network issues were blamed on serious performance problems when several years ago Google apps were introduced by the city of Los Angeles.
'Starting from scratch'
The biggest challenge for BBVA and other firms switching to cloud computing could indeed be cultural issues.
The bank says it has a training programme in place - including personalised guides - to prepare their staff for the move from their tried and trusted email solution and other tools to the new browser-based online world.
However, the bank encourages its employees to leave all their old email and data in those legacy systems. They will be accessible if necessary, but, says Ms Herranz, but we "want to start from scratch... don't want to carry across old behaviours".