The Knicks announced the signing Saturday.
Hardaway, a 25-year-old shooting guard, has spent the past two seasons in Atlanta after spending his first two in New York.
The Hawks will have two days to match the offer, which contains a 15 percent trade kicker and a player option in the fourth year, per ESPN sources.
New York's offer sheet includes an unusual provision requiring the team to pay 50 percent of Hardaway's annual salary by Oct. 1 of every season, according to league sources. The Brooklyn Nets included the same language in their offer sheet for Otto Porter Jr., sources said.
Hardaway, 6-foot-6, had a breakout season in 2016-17 for Atlanta, scoring 14.5 points in 28 minutes per game.
In particular, Hardaway flourished after the Hawks traded Kyle Korver to Cleveland midway through the season. In the final six weeks of the regular season, Hardaway averaged 18 points in 32 minutes per game, hitting 38 percent of his 3-point attempts.
New York, under then-team president Phil Jackson, traded Hardaway on draft night in 2015 in exchange for the rights to point guard Jerian Grant.
Hardaway thrived offensively but struggled at times on defense in New York, which selected him in the first round of the 2013 NBA draft.
He has become a more well-rounded player with the Hawks, who transformed him by initially benching him and sending him to the NBA's D-League. Hardaway eventually developed into a key rotation player for Atlanta and started games for the club late in the regular season and in the playoffs.
Hawks coach Mike Budenholzer said retaining Hardaway was a priority for Atlanta entering the offseason.
If the Hawks elect not to match the offer sheet, Hardaway will return to New York, which would then face a decision with incumbent shooting guard Courtney Lee.
Lee, a nine-year veteran, has three years remaining on the four-year, $52 million contract he signed with the Knicks as a free agent last season.
This is the Knicks' first major move in free agency under general manager Steve Mills, who is the club's top decision-maker in the wake of owner James Dolan's decision to part ways with Jackson late last month.
The Knicks have told agents and rival executives that other priorities in free agency include trying to trade Carmelo Anthony and finding a point guard to help ease the NBA transition for rookie Frank Ntilikina, whom New York selected with the eighth overall pick of the 2017 NBA draft.