Nazarbaev's press service said on January 21 that Tazhin was being transferred to another post but gave no details.
No reasons were given for Orazbaqov's dismissal.
A presidential decree appointed Karim Masimov, the chief of the presidential office, as acting state secretary.
Tazhin, who started working as Kazakhstan’s state secretary a year ago, had previously served as the country's foreign minister, security council secretary, and national-security-committee chairman.
Masimov was Kazakhstan’s prime minister between 2007 and 2012.