Linus Torvalds is infamous for having stated 'If Microsoft ever does applications for Linux it means I've won.' If we measure his success simply based on this fact, then it is clear he has won handedly. Microsoft is currently releasing much of their product line to be compatible with Linux distributions to try to get a piece of the licensing revenue. But in many regards I think Linux has surpassed the wildest expectations that Linus originally had for his Unix based OS.
The most obvious validation of the Linux OS achievement can be seen via the percentage of the world's super computers running Linux. As of November 2015, TOP500 reports 98.8% of the world's fastest 500 super computers run Linux as their OS (TOP500 wikipedia reference). Despite these supercomputer engineering teams having nearly infinite resources to develop the fastest computers, they have elected to use Linux rather than build proprietary systems. Linux is lightweight, easily extensible, and familiar to an immense portion of the computer science community. These advantages make it the clear choice for building modern supercomputers.
The next clear indicator of Linus's tremendous success is the widespread adoption of Linux to the mobile platform. Mobile technology has given the masses cheap and ready access to digital information. Linux is currently dominating this sphere of computing as well, with 80.7% market share thanks to the modified Linux kernel powering Android (OS market share reference). Tens of millions of Android devices are in the pockets of people worldwide.
Finally, and perhaps most fittingly, the greatest indicator of Linus's success is evident in the percentage of developer mindshare that Linux enjoys. The github repository actually shows infinite collaborators (Linux Repository). It is estimated that since 2005 over 11,000 individuals across 1300 companies have contributed an average of 3100 lines of code per day to the Linux kernel making it the largest and fastest growing software project in the world (Linux by the numbers). Microsoft is actually the 21st largest contributor to the Linux kernel by company, contributing approximately 1% of the total kernel.