Three separate productivity apps are available – Word, Excel and Powerpoint – each of which has been optimised for touch-based controls.
Within hours of the launch, Word became the most downloaded application for iPads in Apple’s app store.
The Excel and Powerpoint apps were the third and fourth most popular free app downloads, respectively, in the store.
The popularity shows that customers are interested in accessing Microsoft’s signature Office products in their new, easier to use incarnation, compared with the web-based alternatives provided before.
The firm has faced criticism for not offering the software until now.
Mr Nadella said that the announcement was part of a strategy to empower people “to be productive across all devices” with Microsoft software.
“We are taking great focus and great care to make sure Office on any device shines through,” he said, indicating that his firm would release versions of the apps for other mobile devices in the future.
Research firm Gartner predicts about 271 million tablets will be shipped this year – only slightly less than its forecast of 277 million PCs and laptops – and Apple’s iPad is currently the bestselling model.
Mr Nadella’s predecessor, Steve Ballmer, launched an iPhone version of Office last year and confirmed an iPad version was in the works.
But many industry watchers have speculated that Mr Ballmer deliberately delayed its release in order to debut a tablet touch-centric version on Microsoft’s own Surface machines before bringing it to a competing platform.
Office remains Microsoft’s cash cow, accounting for $16.2bn (£9.7bn) – or just over 60% – of Microsoft’s operating profit in its last financial year. But some believe that sum could have been larger.
“It was definitely a major mistake to wait – an example of the insular old-world thinking of Steve Ballmer and his management team that believed everything should be within a Windows ecosystem,” said Chris Green, from the Davies Murphy Group consultancy.
“In today’s multi-device environment, where Windows is no longer the all dominant platform it once was, that game plan doesn’t work anymore.
The fact Microsoft is now catching up is only going to be a good thing and will be to the benefit of the Office applications.”
The iPhone version has attracted a relatively low review score from Apple’s App Store users, many of whom complained about its cost – it required an Office 365 subscription sold for £80 a year – and missing features.
Meanwhile other apps – including Documents to Go, HopTo, Quickoffice, Google’s business web apps and Apple’s iWork suite – have prospered offering free or cheaper alternatives that can load and alter files originally created by Office.