58-year-old Halimah, an Indian-origin Muslim, would be resigning as Minister of State (MOS) on January 13 as office holders cannot be elected Speakers, said Lee in a statement.
Halimah, a former labour lawyer, is a member of Parliament from the ruling People's Action Party (PAP).
The Speaker's post fell vacant when Palmer, also a PAP MP, resigned last month for his involvement in an extra-marital affair.
Halimah would be confirmed as Speaker as PAP has an absolute majority in the 99-member house.
Lee said he has briefed PAP MPs and received their full support on his intention to nominate Halimah to the position.
Halimah, a mother of five, entered politics in 2001.