Governor Arif Mohammed Khan administered Rajesh the oath of office and oath of secrecy at a solemn function held at the Raj Bhavan auditorium in the morning.
Vijayan, his Cabinet colleagues, and Chief Secretary VP Joy were among those who were present at the event.
Rajesh is replacing MV Govindan, who held the portfolios of Excise and Local Self Governments.
The post became vacant when Govindan was chosen by the ruling CPI(M) as its state secretary, replacing ailing Kodiyeri Balakrishnan. Rajesh will hold the same portfolios as Govindan before him.
A shorter state Assembly session will be held on 12 September at 10 am to elect the new Speaker.
Officials said the session would be held as a continuation of the one that ended on 1 September.
Though the session concluded, the Cabinet did not prorogue the session. Therefore, the additional day would be calculated as a continuation.
If the Congress-led Opposition decides not to field any candidate against LDF nominee AN Shamseer, the election procedure will be over in an hour.
If it fields a candidate, a secret ballot election will be conducted. The session will conclude after the new Speaker addresses the assembly.