ASJ -- a 28-year-old former Buccaneers, Jets and Jaguars tight end -- was pulled over in Gig Harbor, Wash. on March 9 at around 1 AM after cops say they saw him doing 48 MPH in a 30.

In police documents, obtained by TMZ Sports, cops say ASJ was also swerving in his 2016 Dodge Charger ... and nearly turned onto a wrong-way offramp before he cut across multiple lanes of traffic without a blinker.

In the docs, police say when they questioned the ex-NFL player ... he reeked of booze and burnt weed. Cops also say they noticed he had red, bloodshot eyes.

Police say ASJ refused to take field sobriety tests ... so they arrested him -- and prosecutors ultimately charged him with 1 count of DUI, 1 count of driving with a suspended license, and 1 count of operating a vehicle without an ignition interlock device.

FYI -- the order for the device appeared to stem from a previous DUI arrest -- Seferian-Jenkins had been busted for DUI twice before ... once in 2013 and again in 2016.

Seferian-Jenkins battled the most recent charges in court for the past nine months ... but according to a court official, ASJ cut a deal with prosecutors this week.

The court official tells us Seferian-Jenkins took a deferred prosecution deal from prosecutors ... essentially, Seferian-Jenkins agreed to keep his nose clean for five years, complete a 2-year outpatient treatment program, attend a victim impact panel and pay fees.

In exchange, the court official says prosecutors agreed to drop the charges in 5 years if ASJ completes all of the above.

Seferian-Jenkins is due back in court in Dec. 2022 to make sure he's completed the 2-year outpatient program.

ASJ had an up-and-down career after getting picked by the Bucs in the 2nd round of the 2014 draft ... he played in just 43 games, totaling 1,160 receiving yards and 11 receiving TDs.