Appearing at the factory with team boss Toto Wolff, Bottas promised to push new team mate and triple world champion Lewis Hamilton as hard as possible.
"I'm sure we are going to be close and both pushing each other forward," said the 27-year-old, who has yet to win a grand prix in four years at Williams but has appeared on the podium nine times.
Wolff, who helped guide the Finn's early career and also has close ties with Mercedes-powered Williams as a former shareholder, said Bottas would fit in well.
"He's very fast as a driver, and he shows our values," added the Austrian, who has had an unexpectedly busy winter following Rosberg's shock decision to quit 45 days ago, less than a week after winning his first championship.
"He's modest, humble and hard-working."
Williams had earlier announced that Massa, who left at the end of last season at the age of 35, had agreed a one-year contract to end the shortest of retirements.
Mercedes have been dominant for the last three years, winning both the drivers and constructors' titles, and will start as favourites again despite major aerodynamic rule changes.
