Crooks, 30, whose existing deal at the Riverside ran until June 2025, has joined the US side for an undisclosed fee and has penned a three-year deal.
The Leeds-born player, who started his career at Huddersfield Town, joined Boro from Rotherham United in the summer of 2021 and made 115 appearances for the club, scoring 23 times.
The Millers inserted a sell-on clause into the deal in case of a future move and are to benefit following the midfielder’s switch to the States.
Crooks – whose nickname at the club was ‘Tree’ – was a popular and instrumental figure in his time on Teesside and has penned a farewell letter to supporters.
It read: “When first joining, I remember saying ‘it’s Middlesbrough’, and I haven’t been disappointed, what a club.
“Only six months ago, I described this place as home and that it will remain.
“But life is short and we only get one go at it, and to have the chance to experience football and life in another country with my family was one I was keen to take up.
“From the very first game, playing as a tricky right-winger at Fulham away, right up to Chelsea in a domestic semi-final, I gave it my all.
“Under each manager came different challenges and plenty of positions, yet all provided me with memories which I am sure I’ll be able to look back on fondly.
“Reading at home, United away, Spurs at home, Chelsea at home. Fantastic.
“Good luck to everyone involved with the club for the rest of this campaign, I’m sure the lads and staff will give everything ’til the season ends.
“Aside from the football, I must place thanks to you all who have supported the Jordan Sinnott Foundation Trust from the minute I arrived.
“We have been able to raise incredible amounts of money together and I hope you continue to keep an eye on what we do.
“Hair is fine, can’t question it. Belters, all the time? Not sure.
“Up the burrow, (sic) Tree.”