After the two clubs agreed a fee, Green completed a medical at Oakwell on Thursday to end an 18-month stay in Somerset.
The 23-year-old arrived on a free transfer from AFC Bournemouth in August 2017 and went on to make 68 appearances for the Glovers, scoring eight goals.
Green played an important role in Town’s run to the Emirates FA Cup Fourth Round last season, netting in the first and third round to help secure a tie with Premier League giants Manchester United at Huish Park.
Moving into the 2018/19 campaign, the diminutive attacker grabbed a brace in the historic 6-0 win at Newport County in September as part of the club’s biggest ever victory in the EFL.
Jordan’s last act in a Town shirt proved to be scoring the winner in last weekend’s 1-0 win at Mansfield Town, departing Huish Park with the best wishes of all at YTFC.
Manager, Darren Way, said: “As much as I’m disappointed to lose Jordan, I feel extremely proud that he becomes the latest player on a long list that we’ve developed and nurtured.
“We tried extremely hard to secure Jordan’s long-term future but ultimately, we were unable to stand in the player’s way once his heart was set.”