Allen, who co-founded Microsoft along with Bill Gates, is also a part owner of Seattle Sounders FC.
"My brother was a remarkable individual on every level. While most knew Paul Allen as a technologist and philanthropist, for us he was a much loved brother and uncle, and an exceptional friend," Allen's sister, Jody, said in a statement.
"Paul's family and friends were blessed to experience his wit, warmth, his generosity, and deep concern. For all the demands on his schedule, there was always time for family and friends. At this time of loss and grief for us – and so many others - we are profoundly grateful for the care and concern he demonstrated every day."
Allen was among the wealthiest people in the world. His estimated $21.7-billion net worth put him 44th on Forbes' list of billionaires.