Stroll, who turned 18 Saturday, will be making his Formula 1 debut after a three-year run in junior single-seaters, during which he became champion in Italian Formula 4, the Toyota Racing Series and European Formula 3.
The Canadian, who takes the spot of retiring veteran Felipe Massa, has been running a test programme with Williams' two-year-old FW36 car in preparation for his debut 2017 season.
Stroll is to become the first Canadian to start a Formula 1 grand prix since 2006, the year when former world champion Jacques Villeneuve ended his tenure in the category.
"To be honest I don't think it has quite sunk in yet," said Stroll. "I have been focused on F3 in 2016.
"Williams wanted me to focus on F3 and finish off the job properly. Since August we have been talking about opportunities.
"I think Williams has so much history and believes in bringing in talent and to be a part of that history now, I am really excited to be in F1.
"It is going to be really amazing. Being in Melbourne and being in Montreal will be an exceptional feeling. I'm happy to be on the grid."
Finland's Bottas, 27, has been part of the Williams set-up since 2010, having performed test and reserve duties before being promoted to a race seat in 2013.
A nine-time grand prix podium finisher, he will have a third different teammate in Stroll in 2017, having previously partnered Pastor Maldonado in 2013 and Massa in 2014-2016.