The SLC and Sri Lankan sports minister Mahindananda Aluthgamage had warned the player they faced being dropped from the national team if they did not sign new deals by today.
"Twenty two out of 23 players have signed the contracts which makes them available for the selection for Bangladesh test series," SLC chief executive officer Ajith Jayasekera told Reuters.
Mahela Jayawardene, the former captain, is abroad and was the only player not to sign his contract.
"The selection committee met and the team is in the process of approval," Jayasekera added.
The contracts expired at the end of February but the players refused to sign a new contract by Saturday's deadline. The SLC extended the deadline to Monday.
SLC officials and Aluthgamage have said the players were demanding a pay of 75 per cent of the board's total earnings, while a senior cricketer said they were merely opposing SLC's move to cut their terms.
A similar pay dispute threatened to derail last year's Sri Lanka Premier League after the players said they would pull out of the tournament.
Galle hosts the first test against Bangladesh from Friday while the second match is scheduled in Colombo from March 16.
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