Anderson, who was an unrestricted free agent, heads to the U.S. capital after spending a decade with the Ottawa Senators.
He appeared in 34 games with Ottawa last year, posting a .902 save percentage and a minus-7.95 goals saved above average, along with 14 quality starts.
Anderson is the Senators' all-time leader in games played by a netminder by a wide margin (435 to Patrick Lalime's 283). He's also tied with Robin Lehner for the franchise's all-time best save percentage (.914) while playing 349 more contests with Ottawa.
Senators general manager Pierre Dorion confirmed in late September the club wouldn't re-sign Anderson.