Reuters reported in January that plans were in place for new plants in the two countries, awaiting a green light from top management that has now been given.
President Akio Toyoda had been cautious about expanding after Toyota was hit by a capacity glut following the global financial crisis.
The new plants will raise Toyota's annual production capacity by nearly 300,000 cars, the two people said - 200,000 in Mexico and up to 100,000 in China. They declined to be identified because they are not authorized to speak to the media, and said the expansion may be announced formally as early as this month.
The renewed expansion drive by Toyota will put more pressure on rivals such as General Motors Co and Volkswagen AG, in a global automotive industry still burdened by being able to make more cars than it can sell. The increase in global production capacity of up to 300,000 compares with sales of just over 10 million in 2014.
Immediately after the financial crisis, big carmakers were cautious about adding production capacity.
Now, with demand in the United States back at pre-crisis levels and China's auto market growing, albeit more slowly, expansion is back on the agenda.
A Toyota spokesman said nothing had been decided.
The Mexican plant is likely to be based in the central state of Guanajuato, the two people said.
It's set to build the next-generation Corolla sedan for the North American market starting in 2019, they said, confirming a Reuters report last month. It would be Toyota's first passenger car plant in Mexico, where it currently only has a small factory building less than 100,000 Tacoma pickup trucks a year.
In China, the world's biggest auto market, the new plant will be located in the city of Guangzhou. It will produce up to 100,000 Yaris subcompacts a year, starting in 2018, the people said.