Former Volkswagen driver Latvala, who sealed his move last week, and Lappi complete an all-Finnish line-up, joining Juho Hanninen in a Toyota Gazoo Racing squad lead by four-time world champion Finn Tommi Makinen.
Latvala and Lappi will contest all 13 rounds of the 2017 WRC, while recently crowned WRC2 winner Lappi will contest a selected third-car programme starting in the spring.
Latvala said driving for Toyota represented symmetry in his rally career, having first competed in one of the Japanese giant's cars 15 years ago.
"I started my rally career in a Toyota Corolla GT in 2001 and my first competitive outing in a World Rally Car was behind the wheel of a Corolla WRC in 2003 in Estonia," he said.
"So, in many ways, it feels like I'm coming home.
"I'm really happy to join the Toyota Gazoo Racing WRC team from the very start and lead this new adventure with them.
"I feel lucky to be part of this story and I hope we will amass a lot of victories in it."
Latvala tested the Yaris for the first time last week.
Makinen started the car's test schedule in April and has remained at the heart of the development since.
While Toyota CEO and president and Toyota Gazoo Racing chairman Akio Toyoda talked of returning Toyota to the height of the rallying powers that carried it to seven world titles, Makinen's immediate expectations were slightly lower.
"The Yaris WRC is a well-designed car with incredible potential," said Makinen.
"The new regulations allow for much greater freedom in terms of development.
"Although we have yet to explore all the possibilities, we can say that the car is reliable and quick.
"I really can't wait to see the results in racing conditions."
Toyoda joined Makinen at a test earlier this month, enjoying his chance to ride as a passenger.
"Perceiving the car's sound and smell, the feel of the steering wheel and pedals, and, more than anything else, the look on Tommi's face, I was able to share with him a feeling of confidence in our ability to compete with this car," Toyoda said.
"As I said after this year's 24 Hours of Le Mans endurance race, Toyota Gazoo Racing hates to lose.
"Rest assured that the same attitude applies to WRC."
TOYOTA YARIS WRC TECH SPEC
Engine: 1600cc turbo
Torque: 425 Nm
Gearbox: 6-speed sequential hydraulic shift
Differentials: Active centre, mechanical front and rear
Suspension: MacPherson struts, Bos dampers
Brakes: 300mm/370mm discs, four-piston calipers (gravel/asphalt)
Steering: Hydraulic rack and pinion
Wheels: 7x15-inch/8x18-inch (gravel/asphalt)