While the clubs are still to announce the agreement, it will be done before the start of the 2018 World Cup.
It is understood that a €13 million asking price has been agreed for the winger.
The Spanish forward spent the second half of last season on loan at Vicarage Road.
He could only make seven appearances for the Hornets last season though due to injury.
Griezmann’s future has been the source of much speculation over the past 12 months and, after last summer being heavily linked with Manchester United, has since emerged as a possible big-money signing for Barca.
The 27-year-old, who could also decide to shun any suitors and extend his four-year stay with Atletico Madrid, is set to announce his intentions before France begin their World Cup campaign against Australia next Saturday.
Should he decide the Nou Camp is his next destination, Messi believes the prolific striker’s signature will help Barca’s bid to reclaim their former mantle as Europe’s top team from Real Madrid.
Asked if Griezmann is the La Liga champions’ top summer target and if he is the signing they need, Messi told Spanish newspaper Sport: “I don’t know if he’s a priority. I’m in agreement that to get back to winning the Champions League we have to have the best players. And Griezmann is one of them.
“If the club sign him, brilliant. I don’t know if he’s the priority. It depends on the technical secretary and coach.
“I’m just saying that to win the Champions League you need to have the best. And he is very good.”
Messi won the Champions League four times with Barca between 2006 and 2015 but has seen arch-rivals Madrid claim four of the last five editions.
The Argentinian, whose side were surprisingly dumped out of last season’s competition at the quarter-final stage by Roma despite winning the first leg 4-1, said: “The truth is we would like to have won more Champions Leagues, above all in the last three years.
“Getting knocked out at that stage of the competition can’t happen to us, especially how it happened this time, with the first leg lead we had.
“That made the elimination even more painful and it was viewed as being even worse because of how it happened.”
Guardiola, 47, crafted one of the greatest club sides in history when he was installed as head coach from 2008-12. Prior to his decision to take a sabbatical year ahead of moving to Germany’s Bayern Munich, the Catalans swept up three La Ligas, two Champions Leagues, two FIFA Club World Cups, two Copa del Reys, three Supercopa de Espanas and two UEFA Super Cups.
“As a coach it’s over, because I’m not the same, nor is their look towards me the same,” Guardiola told TV3 about the club for whom he was also attached as a player from 1984-2001.
Guardiola was also pressed about whether he would ever return in a higher position.
He replied: “President? No, I’m a coach and I’m good at my job, you can not be good at all of them.
“When I’m done, you’ll find me playing golf.”