Rossi's future had been the subject of intense debate for most of the summer after an impressive loan spell at Parma at the end of last season.
The six-year deal is subject to a medical but is expected to be completed before the end of the week, allowing Rossi, 20, to effectively replace another former United player, Diego Forlan, who enjoyed three productive seasons at Villarreal before leaving for Atletico Madrid last month.
During United's pre-season tour of the Far East, United manager Sir Alex Ferguson had suggested the futures of both Rossi and England international Alan Smith were in doubt as the Carlos Tevez deal edged closer to completion.
Smith is due to open negotiations with Newcastle, as Everton wait in the wings, but, with a date of August 22 now set for a three-day hearing that will determine who owns Tevez's registration, Ferguson has felt confident enough to offload Rossi - a player of undoubted promise who has never really had the chance to fulfil it at Old Trafford.
Ironically, Rossi's last start for United was in the final game of the 2005-06 campaign, when he was preferred to Ruud van Nistelrooy, a decision which effectively ended the Dutchman's Old Trafford career.
Although the Italy Under-21 international did not find the net against Charlton on that occasion, his scoring return of four goals in 14 senior appearances for the Red Devils is better than many, more experienced players have managed.
It was at Parma at the back end of last season where Rossi really came to the attention of top European scouts.
His nine goals in 17 appearances for Claudio Ranieri's men effectively kept them in Serie A.
Ferguson would no doubt have liked to keep Rossi at Old Trafford but he previously acknowledged a need to let the New Jersey-born youngster develop his own career.