Ceballos, a former Barcelona youth player, has signed a three-year contract at The Valley, while Bergdich joins on a four-year deal from Spanish side Real Valladolid for an undisclosed fee.
The duo become manager Guy Luzon’s fifth and sixth additions of the summer, following the arrivals of Ahmed Kashi, Simon Makienok, Patrick Bauer and El-Hadji Ba.
Ceballos joined Barcelona’s famous youth academy in 2004 as an 11-year-old and spent seven years at the club before joining Tottenham Hotspur.
During his four years with Spurs, the Spaniard failed to make a single appearance and was sent out on loan to Portuguese side F.C. Arouca last season, where he made 19 appearances, scoring once.
Left-back Bergdich, 26, began his career at French club Alfortville before moving to Lens and then onto Valladolid. The Morocco international most recently spent time on loan at Serie A side Genoa.
“Cristian is a very technical player, who has a lot of quality and skill and I hope that he will be able to show that to Charlton fans this coming season,” Luzon told the club’s official website.
“He had a strong football upbringing at Barcelona and after joining Tottenham he kept a strong goalscoring record within their development team.”
Luzon added: “We identified Zakarya as a player who possesses a lot of pace on the left side of the pitch, and I’m very pleased that we are able to confirm him as a Charlton player.
“He is an exciting footballer who will excite the Charlton fans and while with Genoa last year he played against some of the hardest opponents in European football.”