The SLC and Sri Lankan sports minister Mahindananda Aluthgamage had threatened to drop the 23 for the series against Bangladesh that starts on Friday if they did not sign new contracts by Monday.
"Twenty-two out of the 23 players have signed the contracts which makes them available for selection," SLC chief executive Ajith Jayasekera told Reuters.
Former captain Mahela Jayawardene, who is abroad, was the only player who did not sign.
The contracts expired last month and the players refused to agree new deals by Saturday's deadline, prompting SLC to give them two extra days.
SLC officials and Aluthgamage said the 23 were demanding 75 percent of the board's total earnings but a senior cricketer said they were merely opposing an SLC 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.
The first Test in Galle begins on Friday and the second match in Colombo starts on March 16.
Sri Lanka included uncapped left-handed batsman Kithuruwan Vithanage, wicketkeeper/batsman Kushal Perera, right-arm spinner Tharindu Kaushal and all-rounder Jeevan Mendis in their 16-man squad for the opening test.
Vithanage, 22, scored an unbeaten 168 against Bangladesh in a three-day practice game while representing Sri Lanka's development team.
Team: Angelo Mathews (captain), Dinesh Chandimal, Tillakaratne Dilshan, Dimuth Karunaratne, Kumar Sangakkara, Lahiru Thirimanne, Shaminda Eranga, Kushal Perera, Jeevan Mendis, Kithuruwan Vithanage, Ajantha Mendis, Nuwan Kulasekara, Chanaka Welagedara, Suranga Lakmal, Rangana Herath, Tharindu Kaushal.