The Mestalla outfit will appoint the Serbian to lead the club next season following its failure to secure Champions League soccer.
Valverde only replaced Mauricio Pellegrino back in December, but after narrowly missing out on fourth spot and Champions League soccer next season, his tenure is likely to end this summer.
The 49-year-old already alluded to being uncertain about his future earlier in May, and Valencia's decision confirms his worst fears following the club's 4-3 loss at Sevilla on Saturday.
The man set to be appointed his replacement, Djukic, confirmed on Friday that he would be leaving Valladolid in a bid for a fresh challenge, having guided the club to a 14th place finish this term in his second campaign at the club.
His side's brand of attacking soccer secured promotion from the Segunda Division via the playoffs last season and is believed to have caught the eye of several teams, with Valencia moving swiftly to appoint the 47-year-old.
Prior to joining Pucela in 2011, he enjoyed spells in charge of Serbia's Under -21 and full national side, either side of a brief stint at Partizan, before moving on to Mouscron and Hercules.
Djukic spent six years at the Mestalla as a player, winning La Liga, the Copa del Rey, Supercopa and Intertoto Cup, as well as reaching the Champions League final in 2000 and 2001.