Fans of the brain-teaser game, which involves filling in an unfinished grid of numbers, can download 10 puzzles for their mobile phones for £4.50.
Every time the downloaded game is started up, each player is reminded to buy the print edition of the newspaper.
"This is a first for mobile content," Ray Anderson, CEO of Bango, said the mobile specialist, which is working with News International to offer the services for The Times.
"Sudoku is perfect for the mobile phone," he added. "A lot of people have their mobile with them when they want to kill time with a game like this. The Sudoku board fits the current screen sizes and, of course, it is all about numbers."
The mobile game even has a "cheat" mode, which can allow the player to uncover the true number for each part of the grid.
Bango's technology "enables The Times to engage the user this way and to sell to them when they want to buy the game," Anderson explained.
With the Bango Txt Trigger service, people can access the Sudoku mobile internet site which was created by Blue Star Mobile by texting "sudoku" to 85080.
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