Roslyakov had gone on a shooting spree in the college before committing suicide, the committee said, and could be seen beforehand on CCTV entering the school with a rifle.
Teenagers and staff were among the dead, the teacher added, and at least 50 people were injured in the attack.
He said police arrived about 10 minutes later to evacuate people from the college and he saw dead bodies on the floor and charred walls, presumably from some fire or explosion.
Dmitry Peskov, the spokesman for Russian President Vladimir Putin, told reporters that officials are looking into a possible terrorist attack.
Russian news agencies quoted a senior official with Russia's National Guard, a law enforcement agency, as saying that the attack was being treated as terrorism. Kerch is located on the peninsula where a bridge links Russian Federation and Crimea, Reuters reported. Russia's Defence Minister Sergei Shoigu said the military was sending forces and supplies to help the victims.
The Telegram channel 112 identified the man as Vladislav Roslyakov, an 18-year-old fourth-year student of the polytechnic college.More news: 'SNL' skewers freaky Trump, Kanye Oval Office meeting
According to a source cited by the RIA Novosti state news agency, Roslyakov had legally acquired a gun licence and passed the necessary psychological tests to do so.
Another student, Semyon Gavrilov, told the Komsomolskaya Pravda newspaper that he saw "a young man with a gun walking around shooting everybody", and how he himself had survived by hiding in a classroom. Russian explosives experts later inspected the school for other possible bombs.
A mass shooting on October 17 at a college in Crimea, which Russian Federation annexed in 2014 from Ukraine, left 18 dead and dozens of others wounded. It was not immediately clear if the alleged attacker had detonated the explosive device. "I would have been dead now", she said.
Another witness who gave his name as Sergei and who worked nearby said in a video on the Kerch.tv website that he heard "a bang and shots".
The attack drew parallels to the 1999 Columbine High School massacre in the United States in which 12 pupils and a teacher were killed - with some saying the shooter used it as inspiration.
"Only three minutes ago I received information about what happened in Kerch, Russia, and I declare the deepest sympathy on my behalf and on the behalf of the Serbian people", Vucic said, according to TASS.
Was the Kerch college attacker inspired by the infamous Columbine massacre in the US?