Ex-convict Yuri Zarutsky, who splashed the acid in Filin's face, was sentenced to 10 years; a driver, Andrei Lipatov, got four years.
The three were also ordered to pay 3.5 millions rubles (about $106,000) in damages to Filin.
Judge Yelena Maximova ruled that Dmitrichenko and two other men had made plans to hurt Filin a few months before the attack.
The dancer said during the trial that he had agreed to Zarutsky's offer to beat up Filin, but claimed that he had been unaware of his intention to use acid for the attack. He pleaded not guilty but admitted "moral responsibility" because he spoke badly of Filin in front of Zarutsky.
As the judge announced the sentence, Dmitrichenko's mother covered her mouth. The dancer's father said they expected a less severe sentence.
Lawyers said they would appeal.
In his testimony, Filin called Dmitrichenko a volatile and threatening employee who was always stirring up trouble, but stopped short of accusing him of plotting the attack.
Dmitrichenko said he was shocked when he heard about the acid attack in the news and told Zarutsky they should surrender to the police. He testified that Zarutsky told him to keep silent and threatened to launch a similar attack on Dmitrichenko's ballerina girlfriend if he went to the police.
The judge accepted that Dmitrichenko was unaware of the plan to use acid, but ruled that the dancer had been involved in making advance plans for the attack and had given Zarutsky the location of Filin's home and called him right before the attack.
During the trial, Dmitrichenko had claimed he was passed over for the best parts in the theater.
He said he had told Zarutsky that he disapproved of Filin's management style. He insisted that he always said Filin had been an excellent dancer, but he blamed him in part for the negative atmosphere in the theater. He cited several incidents in which troupe members were driven to tears during heated conflicts with Filin.
Filin did not deny the incidents but retorted that it was simply part of the "artistic process."