Stroll, 18, has spent 2016 as one of the Grove-based team’s development drivers, combining the role with a title-winning campaign in the FIA European Formula 3 Championship. He replaces Felipe Massa, who is retiring at the end of the current campaign.
Bottas, meanwhile, will stay on at Williams for a fifth successive season, the Finn having made his debut with the team in 2013.
Williams' announcement brings the number of unconfirmed seats for 2017 down to eight. Three teams - Haas, Sauber and Manor - are yet to confirm either driver, while Force India and Renault both have one vacancy.
Stroll, who is set to become the first Canadian to compete in F1 in over a decade, admitted 2017 will be a steep challenge - but one he feels ready for.
"2017 is going to be a big learning curve for me, but I believe contesting the FIA European Formula 3 Championship for the past two years has prepared me well for the step up," he said.
"I've been experiencing a 2014-spec Williams FW36 since August, which has gone very well. The power is incredible. I'm learning about the car, the incredible downforce, DRS and tyre management, finding a rhythm and finding the limit. I'm becoming more comfortable and confident with each run.
"I'm eager to absorb everything Williams can share with me so that I improve. I'll be taking things on a race-by-race, lap-by-lap basis and hopefully progress with experience like I did when I entered Formula 4 and then Formula 3. I've enjoyed success in karting, F4, Toyota Racing Series and most recently F3 - winning every category I've competed in -so I believe I have earned a shot in F1."
Bottas, meanwhile, said he has unfinished business with Williams - and believes the 2017 regulation changes offer a perfect opportunity for the team to surge up the competitive order once more.
"It's going to be an exciting year with all the regulation changes and a great opportunity for the team to get closer to the front," said the Finn, who has scored nine podiums over the last three seasons with Williams.
"I'll be giving 100 percent as always to the team. Thank you to Frank, Claire and the whole Williams Board for their continued trust in me. Also, thank you to everyone at Williams, as it will be nice to continue working together with everyone both at the factory and the track. I'd also like to extend a very warm welcome from myself to Lance on joining the team. I look forward to seeing what we can achieve together.
"Williams is like my family. Going into next season, it will be eight years in total since I joined at the start of 2010, so it really does feel like home here. However, I still believe we haven't yet achieved what we should, and can do together."
Deputy team principal Claire Williams hailed Williams' 'fresh' new line-up, adding: "I'm delighted to confirm that Valtteri will be racing for Williams once again next year, and be joined by Lance Stroll.
"Valtteri is a much-loved member of the team and his talent is unquestionable, so for him to use that experience to help lead the team forward is exciting. He has played a pivotal role in the team's turnaround since 2014 and we are looking forward to continuing the strong relationship we have with him into the future.
"Lance joined the Williams Young Driver Programme at the end of 2015 and has impressed our engineers with his maturity, talent and enthusiasm. We are pleased to be able to offer him the opportunity to step up and show what he can do in Formula One, after proving a dominant force in all the categories he has raced in so far. He is still young, and we looking forward to seeing him develop as a driver. Williams has a great record of introducing young drivers to Formula One, who have achieved great results, and we hope this will be the start of a long successful career for Lance as well.
"As a team, we continue to push forward in our goal to win races and championships, and believe this exciting fresh combination will put us in a strong position to deliver on our future targets."