League sources told ESPN the deal is for the veteran's minimum, which is $2,116,955, according to ESPN's Bobby Marks.
Beasley, originally drafted by the Miami Heat in 2008, averaged 9.4 points and 3.4 rebounds in 16 minutes per game last season for the Milwaukee Bucks. He shot a career-high 54.5 percent from the field while taking 7.3 shots per game.
The Knicks are Beasley's sixth team in 10 seasons.
It is unclear where the 6-foot-9 Beasley will fit on the Knicks' depth chart. If the organization executes a trade of Carmelo Anthony, Beasley could play significant minutes at small forward for New York.
With Ramon Sessions also officially signing his deal, the Knicks have 15 NBA contracts on their roster and one player -- Luke Kornet -- on a two-way contract. Unless they release a player, New York will have room for just one more two-way contract.