Lim said he was supposed to be sworn in today but outgoing chief minister Tan Sri Dr Koh Tsu Koon had asked it to be delayed by a day.
Lim, who pledged to head a fair and open government, said he would be sworn in after the DAP and Parti Keadilan Rakyat form the state government with more than a two-thirds majority.
The DAP won all 19 state seats it contested in Penang while PKR won nine and Pas managed to win one, bringing to 29 the total number of seats won by the opposition alliance. There are 40 state and 13 parliamentary seats in Penang. The DAP won seven parliamentary seats and PKR won four.