Midfielder Moder, 21, joins on a five-year deal from Lech Poznan and has been loaned back to the Polish club. Legia Warsaw defender Karbownik, 19, has joined on a four-year deal and has also been loaned straight back for the rest of the season.
UEFA Europa League: Arsenal drawn with Eintracht Frankfurt of Germany and 10-time Belgian champions Standard Liege in Group F
Manchester United, Europa League winners in 2017, will face Astana of Kazakhstan as well as Partizan Belgrade and former finalists AZ Alkmaar of the Netherlands in Group L.
Indian Super League: Chennaiyin FC sign fresh two-year deal with Brazilian midfielder Raphael Augusto
Raphael Augusto, former DC United and Legia Warsaw player, has already made 26 appearances over two ISL seasons and won several individual awards.
Tuesday's Champions League action will see Cristiano Ronaldo goes back to first club Sporting Lisbon and Tottenham Hotspur face a crunch trip to Monaco.
Real Madrid coach Zinedine Zidane cursed his side's carelessness after the European champions threw away a two-goal lead against Legia Warsaw and needed a late equaliser from Mateo Kovacic to salvage a 3-3 draw on Wednesday
Champions League: Zinedine Zidane says he can still improve ahead of 100th match as Real Madrid boss
Zidane has won 33 of his 42 matches since replacing the sacked Rafael Benitez in January with seven draws and just two defeats.
Here's a look at all the teams in action in the Champions League on Tuesday.
AS Roma suffered a major European humiliation on Tuesday, when they had two players sent off, losing 3-0 at home to Porto and missed out on the Champions League group stage