Under the agreement for Rodgers, Green Bay will trade their 2023 first-round draft pick (15th overall) and their fifth-round pick for the Jets' first-round pick (13th overall), second-round and sixth-round picks, according to ESPN.
"Obviously, we're comfortable with how this deal shaped," Douglas told a news conference.
"I don't think anyone ever walks away from a negotiation where you feel like you won everything in terms of what's gone back and forth.
"Our goal from the beginning was to add Aaron to the team, so we were able to get that. We agreed to terms yesterday and we're just excited to bring him here."
Rodgers has previously toyed with retirement, but the 2011 Vince Lombardi Trophy winner changed his stance in March when he said he would like to play for the Jets, who have not reached the post-season in 12 years, the longest active drought in the NFL.
The deal will also see Rodgers reunite with offensive coordinator Nathaniel Hackett, with whom he was paired in Green Bay when he won back-to-back MVP awards in 2020 and 2021.
"Really, you felt honoured back a few weeks ago when Aaron said he wanted to be a New York Jet. You felt good," said Douglas.
"He's not very far removed from back-to-back MVPs. His relationship with Nathaniel (Hackett) and some of the other players, we feel he can get comfortable quickly."
The Jets finished the season with a 7-10 record after a six-game losing streak. Rodgers is expected to boost a young team that includes Offensive Rookie of the Year Garrett Wilson and Defensive Rookie of the Year Sauce Gardner.
