Under the government's plan, the law, which will be sent to parliament for deliberation, would see gambling take place in large-scale entertainment complexes.
Casinos and most forms of gambling are illegal in Thailand but soccer betting and underground gaming activities and lotteries are rife, with vast sums of money changing hands.
Only some gambling is permitted, such as state-controlled horse races and on an official lottery.
Neighbours, Cambodia, Singapore, the Philippines, Laos and Myanmar have benefited from large casino complexes and Thailand's government has argued the absence of legal casinos means it is turning its back on revenue and not reaching its tourism potential.
Tourism is a key driver of Southeast Asia's second-largest economy and Thailand is forecasting record visitor numbers in the next few years.
"Legalisation will protect the public and would also generate more state revenue," Paetongtarn told reporters.
Successive Thai governments have sought to legalise and regulate gambling to boost the economy but each attempt has faced pushback from conservatives in the Buddhist majority country.
The latest move could see foreign visitor numbers grow 5% to 10% and tourism revenue increase by about 120 billion baht to 220 billion baht ($3.45 billion to $6.32 billion), said Deputy Finance Minister Julapun Amornvivat.
About 9,000 to 15,000 new jobs would be created, he added.
A key advocate of legalising gambling has been billionaire former premier Thaksin Shinawatra, Paetongtarn's father, an influential figure in the ruling party.
