For the last several months, Yahoo has been battling revelations of massive security breaches.
In addition, congressional committees are investigating possible links between Russian figures and associates of President Trump.
USA prosecutors may never get their hands on Dokuchaev, Sushchin and Belan, all of whom are protected in Russian Federation.
The FSB officers "protected, directed, facilitated and paid criminal hackers to collect information through computer intrusions in the USA and elsewhere", the department said in a statement announcing the indictments.
The hack targeted the email accounts of Russian and US officials, Russian journalists, and employees of financial services and other businesses, officials said. After two years, the attackers lost access to Yahoo's networks in September 2016, but stolen data continued to be used until at least through the end of last year, they said. "We would hope they respect our criminal justice system, and respect these charges and what they need to do", Head of National Security at the U.S. Justice Department Mary McCord said.
After the Chinese military hackers were indicted, officials said their activity seemed to dwindle.
Experts admit the U.S. also uses hackers, sometimes to help find other cyber criminals, but Washington is far more cautious than it used to be about alerting Moscow to their presence.
Baratov was one of four suspects arrested Tuesday in connection with the U.S. Justice Department investigation into the cyberattack that compromised more than half a billion user accounts.
The indictment says that Dokuchaev and Sushchin paid, directed, and protected two known criminal hackers who took part in the scheme-Alexsey Belan, a Russian national and resident, and Karim Baratov, born in Kazakhstan and a naturalized Canadian citizen and resident.
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The White House has asked those committees to also investigate Mr Trump's unverified wiretapping allegations against Mr Obama. He added in a subsequent tweet: "How low has President Obama gone to tapp my phones during the very sacred election process".
In a rare move, the USA has indicted two Russian government agents for their suspected involvement in a massive Yahoo data breach. The hackers also filched the firm's source code and proprietary technology to manage users' accounts and password changes.
Belan, also known as "Magg", was born in Latvia but holds a Russian passport, according to the Federal Bureau of Investigation. He was arrested in December in Moscow, according to the news agency Interfax, on charges of state treason for passing information to the CIA.
Ministry of Transportation documents show that Baratov has, at various times in the past five years, affixed his "Mr Karim" vanity license plate to an Aston Martin, a Porsche, an Audi, a Lamborghini, a Mercedes Benz and three BMWs.
The FSB press service had no immediate comment on the indictment, and the agency did not reply to earlier faxed questions about its broader contacts with hackers.
According to the indictment, instead of detaining Belan, who had been named to the FBI's Cyber Most Wanted list in November 2013, Dokuchaev and Sushchin enlisted his help to gain unauthorized access to Yahoo's network.
"Rather than do that type of work, they actually turned against that type of work", McCord said.
In other instances, according to the indictment, the hackers "sought access to accounts of employees of commercial entities, including executives and other managers of a prominent Russian investment banking firm...; a French transportation company; US financial services and private equity firms; a Swiss bitcoin wallet and banking firm; and a USA airline". But according to the Justice Department, the Yahoo hack case is the first time that Russian intelligence officials are being blamed by federal prosecutors for cyber-crime, notes The New York Times. "We are deeply grateful to the FBI for investigating these crimes and the DOJ for bringing charges against those responsible", said Chris Madsen, assistant general counsel and head of Global Law Enforcement, Security & Safety at Yahoo.
The four will face a total of 47-count charges, ranging from conspiracy, computer fraud, and abuse, to economic espionage and aggravated identity theft.
Chief executive Marissa Mayer tweeted that Yahoo was "very grateful to the FBI & DOJ" for their work.