Petrov and Boshirov were charged in absentia by Britain in 2018 for trying to kill former Russian spy Sergei Skripal and his daughter, Yulia, with the Soviet nerve agent Novichok.
He said the Czech Republic, as a sovereign state, had to react to those findings.
Czech Prime Minister Andrej Babis said the move is based on "unequivocal evidence" provided by the Czech intelligence and security services that points to the involvement of Russian military agents in the massive explosion in an eastern town that killed "two innocent fathers".
The expelled, who were allegedly "identified as members of the Russian secret services", will have to leave the Czech Republic within 48 hours, said Czech Interior Minister and also acting Foreign Minister Jan Hamacek.
Separately, Czech police said on Saturday they were searching for two men carrying various passports, including Russian ones in the names of Alexander Petrov and Ruslan Boshirov.
Foreign Secretary Dominic Raab said: "The UK stands in full support of our Czech allies, who have exposed the lengths that the Russian intelligence services will go to in their attempts to conduct unsafe and malign operations in Europe".
The US said it was expelling 10 diplomats from the Russian Embassy in Washington DC on Thursday in response to a cyber-attack as well as other Russian activities.
Several explosions shook the Vrbetice ammunition depot, 330 km southeast of Prague, on October 16, 2014. He added that the country's president, Miloš Zeman, who is close to the Kremlin, had been informed of the situation and had expressed his "absolute support".
The Czech Republic "has apparently chose to close its embassy in Moscow" by expelling 18 Russian diplomats, the Interfax news agency quoted an unnamed diplomatic source as saying on Saturday.
Following the attack in England, investigative journalists identified Petrov and Boshirov as aliases for Russian military intelligence officers named Alexander Mishkin and Anatoly Chepiga.
"I have instructed our ambassadors at the European Union and North Atlantic Treaty Organisation to inform our allies about the Vrbetice case".
These are the same names used by two Russian intelligence officers the United Kingdom says carried out the poisoning in Salisbury, Wiltshire in 2018.
The pair then switched to one Moldovan passport in the name of Nicolai Popa, born July 18, 1979 and a Tajikistan passport in the name of Ruslan Tabarov, born October 23, 1975.
They said the two also visited the capital of Prague and another northeastern Czech region.