A judge announced the sentence after convicting Dmitrichenko and two co-defendants of the attack on Sergei Filin last January.
The attack exposed poisonous rivalries over roles, money and power at one of Russia's most prominent cultural institutions.
Yuri Zarutsky, who admitted to being the masked attacker who threw acid in Filin's face in January, was sentenced to 10 years in prison. Andrei Lipatov, who drove Zarutsky to the scene, was sentenced to four years.
Judge Yelena Maximova said Dmitrichenko and two co-defendants had intentionally caused grievous bodily harm.
"Their guilt in committing the crime has been established in full," she said.
Handcuffed in a courtroom cage with Zarutsky and Lipatov, Dmitrichenko smiled and looked over at his father as Maximova finished reading out the verdict, which took three hours, and announced the sentences.
Lawyers for all three defendants said they would appeal.
Filin has said he can never forgive his attackers but his lawyer, Natalya Zhivotkova, indicated she was satisfied. "Six years is a big punishment," she said outside the courthouse.
The judge also ordered the trio to pay a total of 3 million roubles (£55,032) in moral damages and 508,000 roubles (£9318) in material damages, as requested by Filin.
Prosecutors had asked for nine years for Dmitrichenko, 10 for Zarutsky and six for Lipatov.
The attack left Filin, 43, writhing in pain in the snow as he returned to his apartment building from the theatre late one evening.The judge said Filin had grabbed Zarutsky's hand after he splashed the acid, but the assailant broke free and fled.
Maximova said testimony showed that Dmitrichenko had offered Zarutsky 50,000 roubles (£917) to give Filin a beating, and had tipped him off by telephone that Filin was on his way home.
Dmitrichenko, who joined the Bolshoi as a teenager in 2002 and made his name playing villains such as the murderous tsar in the ballet "Ivan the Terrible", has acknowledged he wanted Filin roughed up but said he had not expected acid to be used.
Zarutsky, who pleaded guilty, has said it was his own idea to use acid, and that he did not tell Dmitrichenko of his plan.
The prosecution said in court that Dmitrichenko had been motivated by a conflict with Filin.
Prominent former dancer Nikolai Tsiskaridze told the court that Filin had denied roles to both Dmitrichenko and his girlfriend, a ballerina.
The case marks one of the worst crises at the Bolshoi Theatre since its foundation in 1776.
The imposing colonnaded building housing its main stage, a stone's throw from Red Square and the Kremlin, only reopened last year after a long renovation dogged by accusations of waste and corruption.
The trial exposed a company riven by feuds and rivalries.
In a courtroom confrontation, Filin said Dmitrichenko had spread false allegations that he had played favourites and had love affairs with ballerinas.
But defence witnesses portrayed Filin as an imperious hothead and Dmitrichenko as a champion of others in the company who feared to speak out against the artistic director, wary of his power to make or break careers.