Allen had announced earlier this month that the disease, which he had been treated for in 2009, had returned.
Allen's sister, Jody Allen, wrote in a statement: "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, who co-founded what became known as Microsoft with his childhood friend Bill Gates, had owned the Seahawks since 1997 and the Blazers since 1988. He's also the co-owner of the MLS' Seattle Sounders FC.
We miss you.— Trail Blazers (@trailblazers) October 15, 2018
We thank you.
We love you. pic.twitter.com/rxkn1IjJ0R
Allen's ownership of the Seahawks coincided with the most successful years in franchise history. It has included 12 trips to the playoffs, three Super Bowl appearances and a victory in Super Bowl XLVIII over the Denver Broncos. When Allen purchased the team, it had only reached the playoffs four times since its inception in 1976.
Allen's purchase of the Seahawks from previous owner Ken Behring saved the team from what had seemed like a near-certain relocation. Behring had announced in 1996 that he was moving the Seahawks to Southern California. Allen agreed to purchase an option for the team that would be triggered only if Washington voters passed a 1997 referendum to foot the majority of the bill for what would become CenturyLink Field.
"Paul Allen was the driving force behind keeping the NFL in the Pacific Northwest," commissioner Roger Goodell said in a statement.
"His vision led to the construction of CenturyLink Field and the building of a team that played in three Super Bowls, winning the championship in Super Bowl XLVIII," he said in the statement. "The raising of the '12th Man' flag at the start of every Seahawks home game was Paul's tribute to the extraordinary fan base in the Seattle community. His passion for the game, combined with his quiet determination, led to a model organization on and off the field. He worked tirelessly alongside our medical advisers to identify new ways to make the game safer and protect our players from unnecessary risk. I personally valued Paul's advice on subjects ranging from collective bargaining to bringing technology to our game. Our league is better for Paul Allen having been a part of it and the entire NFL sends its deepest condolences to Paul's family and to the Seahawks organization."
Seahawks coach Pete Carroll was among several current and former Seahawks who tweeted their condolences and shared fond memories of Allen on Monday, as did Oakland Raiders running back Marshawn Lynch, who helped lead Seattle to its lone Super Bowl victory in 2014.
Deeply saddened by the passing of @PaulGAllen. I'll miss him greatly. His gracious leadership and tremendous inspiration will never be forgotten.— Pete Carroll (@PeteCarroll) October 15, 2018
The world is a better place because of Paul's passion, commitment, and selflessness. His legacy will live on forever.
Big dog rest easy as you go home @PaulGAllen prayers for your family🙏🏾— Shawn Lynch (@MoneyLynch) October 15, 2018
"Paul Allen was the ultimate trail blazer -- in business, philanthropy and in sports," NBA commissioner Adam Silver said in a statement. "As one of the longest-tenured owners in the NBA, Paul brought a sense of discovery and vision to every league matter large and small. He was generous with his time on committee work, and his expertise helped lay the foundation for the league's growth internationally and our embrace of new technologies. He was a valued voice who challenged assumptions and conventional wisdom and one we will deeply miss as we start a new season without him. Our condolences go to his family, friends and the entire Trail Blazers organization."
In 1988 at the age of 35, Allen bought the Trail Blazers. He told The Associated Press that "for a true fan of the game, this is a dream come true.''
Allen could sometimes be seen at Seahawks, Blazers and Sounders games or chatting in the locker room with players.
Allen and Gates founded Microsoft Corp. in 1975. Microsoft's big break came in 1980, when IBM Corp. decided to move to personal computers. IBM asked Microsoft to provide the operating system.
The decision thrust Microsoft onto the throne of technology and the two Seattle natives became billionaires. Both later dedicated themselves to philanthropy.
Gates said he was heartbroken about the loss of one of his "oldest and dearest friends.''
"Personal computing would not have existed without him,'' Gates said in a statement.
"But Paul wasn't content with starting one company. He channeled his intellect and compassion into a second act focused on improving people's lives and strengthening communities in Seattle and around the world. He was fond of saying, 'If it has the potential to do good, then we should do it,''' Gates wrote.
With his sister Jody Allen in 1986, Paul Allen founded Vulcan, the investment firm that oversees his business and philanthropic efforts. He founded the Allen Institute for Brain Science and the aerospace firm Stratolaunch, which has built a colossal airplane designed to launch satellites into orbit. He has also backed research into nuclear-fusion power.
Over the course of several decades, Allen gave more than $2 billion to a wide range of interests, including ocean health, homelessness and advancing scientific research.
"Millions of people were touched by his generosity, his persistence in pursuit of a better world, and his drive to accomplish as much as he could with the time and resources at his disposal,'' Vulcan CEO Bill Hilf said in a statement.
Allen was on the list of America's wealthiest people who pledged to give away the bulk of their fortunes to charity. "Those fortunate to achieve great wealth should put it to work for the good of humanity,'' he said.
Allen served as Microsoft's executive vice president of research and new product development until 1983, when he resigned after being diagnosed with Hodgkin's lymphoma.
"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,'' Allen said in a 2000 book, "Inside Out: Microsoft in Our Own Words.''
Allen never married or had children.
Allen's influence is firmly imprinted on the cultural landscape of Seattle and the Pacific Northwest, from the bright metallic Museum of Pop Culture designed by architect Frank Gehry to the computer science center at the University of Washington that bears his name.
Allen also founded an innovative Seattle-based software and production company called Starwave, which played a big part in the mid-90s in getting ESPN onto the Internet. In 1995, Allen's company did a five-year deal with ESPN that allowed his company to license the ESPN name in exchange for $2.5 million a year and revenue split on ads and merchandise. While the site only sold one ad in 1995, a $30,000 three-month ad to Gatorade, according to Starwave CEO Mike Slade, Allen's foresight to use the Internet to make the experience better for sports fans was well before his time.
"I remember in 1993, as we were starting up, Paul asked me how much it would cost to get a sports site off the ground," Slade recalled on Monday night. "And I had no idea, so I just said '$50 million.' And he said, 'OK.' And I was like, 'That's it? Not like, 'Why not $40 million?'"
"And that's why it got off the ground," Slade said. "Because it took an unusual investor, with unlimited funds, who loved sports and didn't care that it was too early to have any business plan."
Information from ESPN's Darren Rovell and The Associated Press was used in this report.