The Finnish striker and the Israeli midfielder were the last of six senior signings made by Neil Lennon during the summer transfer window.
Pukki appeared as a sub for Schalke against PAOK Salonika in the play-off round of the Champions League.
But Uefa's rules now allow a player to play for a second club from the group stage onwards even if he has appeared in the qualifying or play-off rounds.
Both Pukki and Biton are on international duty, and will return to Lennoxtown to train with their new team-mates next midweek.
Clubs can replace three players on the 25-man list for the next stage of the European competitions - the Last 16 of the Champions League and the Last 32 of the Europa League.
Meanwhile, Celtic's Under-19s - under the guidance of John Kennedy - are gearing up for their Uefa Youth League, with Morton's Cappielow to be used for the visit of Barcelona on October 1, while both other home ties will be played at Livingston.