Mr Allen had received treatment in 2009 for non-Hodgkin’s lymphoma and had announced earlier this month that it had returned.
He said he planned to fight his illness once again.
His sister Jody Allen said in a statement: “While most knew Paul Allen as a technologist and philanthropist, for us he was a much-loved brother and uncle and an exceptional friend.”
Microsoft’s CEO Satya Nadella added: “Paul Allen’s contributions to our company, out industry and to our community are indispensable.
“As co-founder of Microsoft, in his own quiet and persistent way, he created magical products, experiences and institutions, and in doing so, he changed the world.
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“I have learned so much from him – his inquisitiveness, curiosity and push for high standards is something that will continue to inspire me and all of us at Microsoft.
“Our hearts are with Paul’s family and loved ones. Rest in peace.”
Mr Allen resigned as executive vice president of research and new product development in 1983 after he was diagnosed with cancer.
The “accidental zillionaire” wrote in his 2000 book, Inside Out: Microsoft in Our Own Words, about the shock he experienced upon being told his diagnosis.
He wrote: “To be 30 years old and have that kind of shock — to face your mortality — really makes you feel like you should do some of the things that you haven’t done yet.”
Mr Allen was part of a list of wealthy celebrities who said they will donate the majority of their wealth.
He said: “Those fortunate to achieve great wealth should put it to work for the good of humanity.”
Mr Allen met Bill Gates while they were studying at a private school in Seattle.
The two eventually dropped out of university together in order to fulfil their goal of putting a computer in everyone’s home.
They achieved a breakthrough in 1980 when they were asked by IBM to design the software for their computers.
Mr Allen and Mr Gates bought another developer’s system and refined it into their own.
This new software became the core for all of IBM’s computers.
They released their first two products, Microsoft Word and Office in 1983.
By 1991, the Microsoft operating system was being used in 93 percent of the world’s personal computers.
The Microsoft operating system became the most-used operating system in the world and the Word programme became the most important in their Office products, quickly putting the two at the head of the technology industry and making them billionaires.