The state cabinet, at its meeting in Shimla, passed a resolution recommending the dissolution of the 68-member assembly.
Admitting defeat, Dhumal told reporters on Friday that he submitted his resignation immediately after the results were announced.
A spokesperson for Raj Bhavan said that the governor was out of town and is expected back late on Friday.
Meanwhile, Dhumal blamed the poor selection of candidates for the BJP's defeat in the assembly polls, the results of which were declared on Thursday.
"There was a problem on the selection of some candidates and the party will shortly analyse to find out where we went wrong," Dhumal said.
The Congress secured 36 seats and the BJP 26 seats, while independents and others bagged six seats.
Prominent losers of the BJP included former ministers Narender Bragta (Jubbal-Kotkhai constituency), Kishan Kapoor (Dharamsala), Khimi Ram (Banjar) and Ramesh Dhawala (Jawalamukhi).