The team announced the deal with the defenseman on Monday.
It has an average annual value of $925,000.
The 18-year-old from Russia was taken with the 31st overall pick in this year's NHL draft. He spent last season in the Western Hockey League.
Alexeyev recorded an assist in a preseason game for the Capitals against the Boston Bruins this month.
He is listed at 6-foot-4 and 199 pounds.