One of the most common technologies for watching video on a computer is now available on smartphones.
Flash software is used to deliver around 75% of online video and is the key technology that drives websites such as YouTube.
Until now, many smartphones and netbooks have used a "light" version of the program, because of the limited processing power of the devices.
The software is intended to work as well on a smartphone as a desktop PC.
The latest version of Flash was unveiled at Google's "I/O" developer conference in San Francisco. Version 10.1 of Flash has been optimised to work on mobiles.
Google was the first maker of a mobile operating system to declare that the technology will work on handsets running its Android software. However, only handsets running the latest version of Android, version 2.2, will be able to use Flash.
Android is available on phones from a range of manufacturers, including Motorola, HTC and Samsung.
"It turns out on the internet, people use Flash. And part of being open means being inclusive, rather than exclusive," said Vic Gundotra vice-president of engineering for Google.
Adobe hopes that Flash 10.1 will soon be available on other mobile platforms such as BlackBerry, Windows Mobile and Symbian. It has given no specific dates for when it will be available on these operating systems.
It said it had worked hard to ensure that Flash on a mobile did not suck up battery power too quickly.
Flash will still not be available on Apple's popular iPhone, which uses a proprietary Apple operating system.
Steve Jobs, Apple's boss, has previously said that Flash had "one of the worst security records in 2009", "has not performed well on mobile devices", and "is the number one reason that Macs crash".
In a reference to Apple's resistance to Flash on the iPhone, Mr Gundotra said: "A special thank you to Adobe for their willingness to work with us and engage with us ... it's much nicer than just saying no."