Peter Johnson, a second submitter who like Mathew was in charge of submitting benchmark interest rates that other trades were based on, had pleaded guilty.
The men are expected to be sentenced on Thursday.
Libor, which stands for the London Interbank Offered Rate, is used as interest rate banks use to lend money to one another.
It is the basis of $450 trillion of contracts and loans globally.
Rate setters conspired to make extra money for themselves and their colleagues by artificially setting rates between June 2005 and September 2007.
Those found guilty told the court that their bosses had sanctioned communications on Libor rates and that requests to rig rates were sent over corporate messaging systems in full view of compliance staff.
The verdict is a victory for the Serious Fraud Office, which has a mixed record at prosecuting white-collar criminals.
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Tom Hayes became the first successful SFO Libor conviction. The former UBS and Citgroup trader was found guilty for his role in Libor last August and is serving an 11-year sentence.
However the SFO failed to get a further six former brokers prosecuted for conspiring with Hayes. Those brokers were cleared in January.
David Corker, partner at Corker Binning, said questions remain about the way in which the Libor prosecutions were brought after loud political pressure.
"They were about conduct widely condoned or encouraged at the time in a broken, poorly regulated system and these defendants were foot soldiers for the most part in a global financial system beyond their full understanding," Corker said.
"The convictions strike the harshest of warnings for those operating at relatively junior levels in financial markets," he added.
Additional reporting by Reuters
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