Mvurya ditched Raila's ODM party for Jubilee Party in the run up to the August elections.
In August, President Uhuru Kenyatta met governors elected on Jubilee Party ticket and its affiliates where they agreed to elect Mr Mvurya as chairman of the Council of Governors.
Mr Mvurya, who defected from the opposition and won re-election, previously served as deputy chairman of the CoG for two terms (four years) under former Bomet Governor Isaac Ruto.
Mr Mvurya is understood to have won over the heart of President Uhuru Kenyatta after he intensified campaigns for his re-election in both in August and October polls.
Kwale deputy governor Fatuma Achani said he is the right person for the post because of his experience as deputy chair of CoG. Mr Mvurya will be deputised by Kirinyaga Governor Anne Mumbi Waiguru.
Mr Mvurya, who is serving his second term as Kwale County Governor, becomes the fourth governor to head the council after former Bomet governor Isaac Rutto, former Meru Governor Peter Munya and Josphat Nanok.
The Kwale boss was re-elected on a Jubilee ticket in the August 8 poll after he ditched ODM.
He expressed confidence of winning saying he is experienced as he served for two terms as deputy chair of the council.
Mr Mvurya vowed to unite governors in the 47 counties if elected and to work closely with the government for development.
Waiguru on the other hand said she believes in herself as a leader and she will deliver effectively because she enjoys support from locals.
While opening the induction conference on Thursday, President Uhuru Kenyatta warned NASA Governors routing for secession that stern action will be taken against them. The induction which begun Thursday will end on Saturday.