Mishra, a 1977-batch Odisha cadre IPS officer, had retired as the chief of the world's largest paramilitary force last month.
Singh, a 1979-batch Uttar Pradesh cadre IAS officer, had retired from service in April last year.
The two advisers to Governor KK Paul were appointed after President's Rule was imposed in the hill state today following days of political uncertainty as nine Congress MLAs revolted against the Harish Rawat-led Congress government.
Speaking to the media shortly after President's Rule was imposed in the hill state, Union Finance Minister Arun Jaitley said there were "cogent, relevant and extremely important grounds" on which the Union Cabinet came to the decision.