ESPN and The Athletic reported the move, which sees Walker leave the Thunder without playing a game.
The four-time All-Star was part of a June trade that saw OKC send Al Horford back to the Boston Celtics and receive the 16th pick in the 2021 NBA Draft.
The Thunder, who are building a young team after trading superstars Russell Westbrook, Paul George and Chris Paul in recent seasons, turned that selection into two more in a deal with the Houston Rockets.
Walker's exit gives OKC more minutes to dish out to prospects and sees the Knicks recruit the starting point guard they badly needed.
Elfrid Payton started 63 games last season but lost his place after 13 minutes, one point and one assist in the playoffs. Frank Ntilikina appeared fleetingly in three postseason games.
Derrick Rose was promoted to a starting role, having rediscovered some form leading the second unit, but the Knicks lost all three of his starts and badly missed his consistent contributions from the bench.
Rose has returned to Madison Square Garden on a three-year, $43million contract yet will likely now serve as back-up to Walker.
Walker is expected to fit into the $10m salary cap space left in New York following the Knicks' free agency business, which included the signing of the guard's former Celtics team-mate Evan Fournier.
Walker, who is only two years removed from an All-NBA Third Team season with the Charlotte Hornets, still had two years and $74m remaining on his previous deal before Wednesday's agreement with the Thunder.
The Knicks will be hoping for an offensive boost from Walker, who was born in The Bronx and went to high school at Rice in Manhatten.
The best defense in the league, giving up only 104.7 points per game, carried the Knicks to the playoffs for the first time in eight years, but they scored only 107.0 points on offense, ranking 26th, and lost to the Atlanta Hawks in the first round.
Walker scored 25.6 points and played all 82 games for the Hornets in a career year in 2018-19, earning the move to Boston.
But a series of injuries kept him from playing or performing consistently for the Celtics, while his usage rate last year fell to 26.3 per cent alongside ball-dominant duo Jayson Tatum and Jaylen Brown.
Walker will get the opportunity to shine again in a prominent role at MSG, as long as he can stay fit.