The deal includes a player option for the fourth year and a 15% trade kicker, Stein adds.
The Kings get two days to match the Hawks' offer for the Serbian guard, or they'll lose him for no compensation.
Earlier in the week, Bogdanovic appeared bound to join the Milwaukee Bucks via a sign-and-trade, but the move was nixed because he reportedly didn't agree to the deal.
The NBA is reportedly investigating both the Kings and Bucks for impropriety, as they worked on the potential deal prior to the league's free-agency window opening.
Bogdanovic, 28, averaged 15.1 points per game last season, shooting 44% from the field and 37% from beyond the arc.
The Hawks have already been busy this offseason, adding Danilo Gallinari, Rajon Rondo, and Kris Dunn.