A Singapore Transport Ministry spokesman said the Bill will support the "construction, operation and regulation" of the Kuala Lumpur-Singapore High-Speed Rail (HSR), in accordance with a bilateral agreement signed last December.
The 350km HSR, which will cut travel time between the two cities to 90 minutes, is targeted to be operational by end-2026.
The Bill will also support the Johor Bahru-Singapore Rapid Transit System (RTS) Link after Singapore and Malaysia ink a bilateral agreement at the end of this year, the spokesman added.
The RTS, which will link Woodlands North station on the upcoming Thomson-East Coast MRT line with Johor's Bukit Chagar, is expected to be ready by end-2024.
In September, rail operators SMRT and Prasarana Malaysia signed a memorandum of understanding to form a joint venture company to finance, build and operate the cross-border MRT line.
Singapore and Malaysia will call a joint tender later this year to appoint an Assets Company for the HSR project.
The appointed company will be responsible for designing, building, financing and maintaining all rolling stock. It will also build, operate and maintain rail assets, including track-work, power, and signalling systems.