Bottas' move to F1's most sought after seat also provided the opportunity for Brazilian Felipe Massa to come out of retirement to replace the Finn at Williams and pair up with Canadian teenager Lance Stroll.
"It's mega to be driving a Silver Arrow this year," Bottas said at Mercedes' factory Monday. "I can't wait to get working properly.
"My goal is immediately at the first race to get all the points that are available. I guarantee I will be giving it all. I want to thanks Toto (Wolff, Mercedes head of motorsport) and everyone at the Mercedes and Daimler boards for this opportunity.
"This is my fifth season in F1. I got nine podiums with Williams, but I'm still missing my first win, so that's my first mission."
Bottas finished the 2016 season in ninth place with 85 points, with his only podium coming as he finished third at the Canadian Grand Prix in June.
New teammate Hamilton, who Rosberg pipped to the world title by five points, endured some frosty exchanges with Mercedes over the course of last season, but Bottas is confident they will perform well as a duo.
"I think with Lewis we are going to be a strong pair together," the 27-year-old said. "I really respect him as a driver and a person.
"I'm sure we are going to close, and we're going to be both pushing each forward. I'm sure we can work as a team."
Veteran Massa, who has 11 grands prix wins to his name, enters into his 15th season in Formula One and his fourth consecutive season with Williams.
"Valtteri has been offered a fantastic opportunity and, as a result, an opportunity arose for me," Massa told Williams F1.
"Going to the current world champions is a great opportunity for Valtteri. He is a talented racer and it was great working alongside him for three years. I wish him all the best for the next chapter of his career.
"I would not have returned for any other team. When I joined Williams back in 2014 I found a team -- and a family -- that I have loved being a part of. I certainly haven't lost the desire to race and fight on track."
Meanwhile, young Mercedes driver Pascal Wehrlein joins the Swiss Sauber team for the 2017 season.
The 22-year-old German, who raced for bottom team Manor in 2016, will partner Marcus Ericsson after being named to replace Brazil's Felipe Nasr on Monday.
The only remaining seats are at Manor, but the British F1 team entered administration in early January and remain unlikely to compete at the start of the 2017 season in March.