The club posted a video on their website of the Serb arriving in Valencia to sign his contract and said he would be presented to the media on Wednesday.
A former Yugoslavia international, Djukic spent six seasons at Valencia as a player and also had stints at Deportivo La Coruna and Tenerife.
As a coach, he helped Real Valladolid win promotion back to the Spanish top flight in the 2011-12 season.
They finished in 14th place last term and he announced at the end of the season he was moving on.
Djukic is well known in Spain for missing a penalty kick late in Depor's final match of the 1993-94 season against Valencia which handed the title to Barcelona.
He said earlier on Tuesday that coaching a club of Valencia's stature was "a dream come true".
"I think we have a very good and very competitive team which is ready to achieve the club's goals," the 47-year-old added.
"I am ready and I have the calm that comes from knowing we have the tools to do great things."
Valverde, brought in to replace Mauricio Pellegrino in December on a six-month contract, said instability at cash-strapped Valencia had convinced him it was best to leave.
They lost 4-3 at Sevilla on the final day of the La Liga season on Saturday and missed out on a Champions League place.
The club has suffered an institutional crisis over the last few months which led to president Manuel Llorente quitting. A replacement is set to be appointed following a shareholders' meeting on Wednesday.
- Sports & Recreation
- Deportivo La Coruna