Sayyari had been at the helm of the Saudi Arabian Monetary Agency (SAMA), the kingdom's central bank, since 1983 when he was appointed acting governor before being confirmed at the post two years later.
Analysts said it was unlikely that Sayyari's departure would lead to a drastic change in SAMA's policies.
The reshuffle did not affect either of the key ministries of oil or finance, official sources said.
The monarch also appointed Abdul-Aziz Khoja, who was ambassador to Lebanon, as information minister, replacing Iyad bin Amin Madani, the television reported, quoting decrees by the king.
Western diplomats say Madani was a strong advocate of reforms in the kingdom. Clerics had often attacked Madani for allowing the local press to take greater liberty in challenging the strong influence of the religious establishment.
Saleh bin Humaid, who was speaker of the advisory Shura Council, was appointed head of the Supreme Judiciary Court and was replaced by the outgoing justice minister, Abdullah al-Sheikh.