Cousins titled the post: "Farewell Washington."
"As I'm about to make one of the bigger decisions of my life, I'll be saying goodbye to my familiar life as a Redskin," he wrote. "After calling Washington home for the past six years, the team has decided to move on to another option and, in turn my family and I will be moving on as well."
The Redskins will trade for quarterback Alex Smith, who is four years older.
"There is no way I would be where I am today, without the leadership of the Redskins organization," Cousins wrote. "Coach Gruden, Bruce Allen, Dan Snyder. Thank you all for the opportunity you gave me.
"When [my son] Cooper someday asks: 'Hey Dad, what's it like playing for the Redskins?' I'll proudly tell him it was a dream come true. Thanks for having me, Washington and thanks for making me into the player I am today."
Cousins, who has played two seasons for the Redskins on a franchise tag, topped the 4,000-yard mark for the third straight year in 2017. He finished with 4,093 yards, with 27 touchdowns and 13 interceptions.
"Knowing I will not be putting on a Redskins jersey next season, it's hard to look back at all that's taken place and not become emotional. I will forever be grateful to Mike Shanahan for taking a chance on me in the 2012 draft.
"At the time, many people saw his selection as foolish. Time proved otherwise and taught me that there are no guarantees in this business -- if you work hard and learn from your mistakes, good things can happen. For the first time in 11 years I will participate in choosing where I play. Having said this, I would not trade the past decade for anything."
The Jets have approximately $90 million in salary cap space while the Vikings could sign Cousins to replace Case Keenum.