The duo have completed their permanent moves to the Istanbul giants and will pocket more than €2m a year as part of Cesare Prandelli's side
The Switzerland international and Macedonian forward entered talks with the Turkish Super Lig giants over the weekend and flew to Istanbul to finalise personal terms and medical tests.
Galatasaray have since confirmed that both players have completed their moves before the closure of the transfer window, with Dzemaili joining for a fee of €2.35 million, while Pandev arrives on a free transfer.
The 28-year-old Dzemaili is set to earn €2.4m for the first year of his three-year deal in Turkey, and €2.1m for the remaining two years. Pandev, meanwhile, will earn the same amount in 2014-15 and will then trigger an extension to match Dzemaili's deal if he plays in 28 games or more for the club.
Dzemaili, who joined Napoli from Parma in 2011, has fallen behind Gokhan Inler, Jorginho and Walter Gargano in the pecking order under Rafael Benitez and was encouraged to look for a new club after returning from World Cup duty.
Pandev, 31, spent two years at the San Paolo after winning a Champions League title with previous club Inter.