Valverde had only resigned from his post at San Mames last week, but wasted little time in finding employment elsewhere, as confirmed by Barca president Josep Maria Bartomeu on Monday.
"He's very happy very excited, he has the ability, experience and knowledge for the job", Bartomeu told a news conference.
"He is a hard worker and he is a fan of using technology in training and in managing matches".
Herrera is reportedly a transfer target for incoming Barcelona coach Ernesto Valverde, but the sources said the 27-year-old - United's Player of the Year this season - would turn down the chance to move to the Camp Nou.
His most successful period came in Greece, where he led Olympiacos to three domestic league titles and two cups in his two stays at the club, while he also guided Espanyol to the UEFA Cup final in 2007, losing on penalties to Sevilla.
One of the sticks with which Luis Enrique was beaten during his third and final season which only delivered the Copa del Rey was his insistence on making Barca a more direct, counter-attacking force. We know him, we know what he can do.
Valverde is a former Barcelona player himself who played under the great Johan Cruyff. It is going to be Ernesto Valverde.
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Andres Iniesta has given his full backing to Ernesto Valverde after he replaced Luis Enrique as Barcelona boss on Tuesday.
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After retiring in 1997 Valverde's coaching career has taken him to Espanyol, Olympiacos, Villarreal and Valencia.
His likely replacement, Valverde, has already announced his departure from Athletic Bilbao, and his arrival at Barcelona now seems inevitable.
Barca finished second in La Liga behind arch rival Real Madrid and exited the Champions League at the quarterfinal stage after being outclassed by Juventus.
He will be presented on Thursday as FC Barcelona coach along with his assistant Jon Aspiazu and former blaugrana Jose Antonio Pozanco who will be the fitness coach.
Athletic thrashed Barcelona 5-1 on aggregate to win the 2015 Spanish Super Cup.