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Flutter Entertainment said it had “long admired” the online bingo firm as it unveiled the all-cash deal.
Tombola’s founder Phil Cronin, who set up the firm 16 years ago, will leave the business after the acquisition, with he and his family expected to net a fortune.
It made underlying earnings of £38.5 million in the year to April 30 on revenues of £164 million.
The deal is set to complete in the first quarter of next year.
Peter Jackson chief executive of Flutter, said: “Tombola is a business we have long admired for its product expertise, highly recreational customer base and focus on sustainable play.
“The brand aligns closely with Flutter’s safer gambling strategy, a key area of focus for us.”
Tombola was the first major UK-focused operator to introduce both mandatory staking and deposit limits.
More than 80% of its revenues come from the UK, with 16% from Italy and Spain.
Mr Jackson added: “As the time comes for Phil to hand over the reins, I would like to thank him for building the success story that the business is today, and I look forward to welcoming the Tombola team to Flutter and growing a sustainable business for the future together.”