* E.ON, RWE, EnBW paid nearly 6 bln eur in fuel taxes
* Verdict to be issued on June 7 at 0730 GMT
* E.ON, RWE shares both up about 1 pct (Adds context, analyst, shares)
DUESSELDORF/FRANKFURT, June 6 (Reuters) - Germany's highest court will on Wednesday announce a long-awaited decision that will ultimately determine whether the country's utilities will get back nearly 6 billion euros ($6.8 billion) in taxes they paid for their use of nuclear fuel rods.
The ruling will be published via a press release at 0730 GMT (0930 CET), the German Constitutional Court said in a statement on Tuesday.
E.ON, RWE and EnBW are pinning their hopes on the verdict as it marks the last chance to challenge the tax after the European Court of Justice in 2015 ruled that it did not breach European Union laws.
Shares in E.ON and RWE were both up about 1 percent following the announcement, with traders pointing to the billions of euros they can claim back should the court rule in their favour.
"There is a good chance of a positive outcome for the utilities," Bernstein senior analyst Deepa Venkateswaran wrote in a note. "We believe that the bulk of the upside is not priced in the stocks."
A fuel element tax, introduced in 2011 and expired in 2016, required firms to pay 145 euros per gram of nuclear fuel each time they exchange a fuel rod, usually about twice a year. E.ON has paid about 2.8 billion euros, while RWE and EnBW have paid 1.7 billion and 1.44 billion, respectively. ($1 = 0.8892 euros) (Reporting by Tom Kaeckenhoff and Christoph Steitz; Editing by Edward Taylor and Michael Shields)