PM Prayuth Chan-ocha admitted that "this decision comes with some risk" - but it is seen as a key step to revive the country's collapsed tourism sector.
The 10 nations seen as low risk include the UK, China, Germany and the US.
Mr Prayuth said Thailand would also allow entertainment venues to reopen on 1 December and permit alcohol sales.
He added that the authorities were planning to open Thailand for more countries on that date.
Mr Prayuth's comments came in a televised address on Monday.
Referring to visitors from 10 low-risk nations, he stressed that "when they arrive, they should present a [negative] Covid test... and test once again upon arrival".
If the second test is also negative, any visitor from those countries "can travel freely like Thais", the prime minister said.
But he warned that the government would act decisively if there were to be a spike in infections or an emergence of a highly contagious variant of Covid-19.
- Covid threat looms over Thailand's plans to open
It is estimated that Thailand - popular for its sandy beaches and non-stop nightlife - lost about $50bn (£37bn) in tourism revenue in 2020.
Just over 70,000 visitors came into the country in the first eight months of this year, compared with 40 million in the whole of 2019.
Thailand has reported more than 1.7 million confirmed Covid cases since the pandemic began, with nearly 18,000 deaths, according to America's Johns Hopkins University.