The sudden border closure in March 2020 left tens of thousands of people stranded on both sides, separated from their families and fearing for their jobs.
Up to 300,000 Malaysians were traveling to the wealthy city-state of Singapore daily before the pandemic.
Malaysian Prime Minister Ismail Sabri Yaakob is also due to pay his first official visit as Prime Minister to Singapore on Monday.
Under the new agreement, up to 1,440 travelers on each side can travel if they hold citizenship, permanent residence or long-term visas in the destination country, without undergoing quarantine, according to guidelines issued by the government of Singapore.
Travelers must test negative for Covid-19 before departure, and Malaysia also requires travelers to pass the Covid-19 test upon arrival. Singapore followed suit on Sunday by demanding an on-arrival test over concerns over the new variant of Covid-19 Omicron.
A vaccinated airlift route between the two countries also began on Monday.
Singapore has vaccinated 85% of its entire population, while Malaysia has vaccinated around 80%.
Singapore, with an aging population of 5.5 million, relies heavily on Malaysians living in the southern state of Johor, which is connected to Singapore by land, to hire staff ranging from restaurants to semi-manufacturing. conductors.
Singapore reported 747 locally acquired Covid-19 cases on Sunday, the lowest tally since mid-September. Malaysia has reported 4,239 cases, the lowest number since early November.