Redknapp, favourite to become the next England manager, denied two counts of cheating the public revenue in relation to alleged payments from former Portsmouth chairman Milan Mandaric into his Monaco bank account totalling $295,000.
Serb Mandaric, now Sheffield Wednesday chairman, also denied the charges before a packed courtroom at London's Southwark Crown Court.
Prosecution lawyer John Black told jurors "both parties must have known" they were avoiding taxes.
"These payments were a bung or offshore bonus that the parties had absolutely no intention of paying taxes for," he said, according to Britain's Press Association.
Redknapp named the account "Rosie 47," apparently a reference to his dog's name and his year of birth.
Redknapp's son and former Liverpool midfielder Jamie Redknapp looked on from the viewing gallery.
The first charge against the duo alleges Mandaric paid $145,000 into Redknapp's Monaco-based bank account between April 1, 2002 and November 28, 2007 to avoid paying income tax and national insurance.
Trial judge Anthony Leonard asked jurors to speak out if they had football allegiances strong enough to prejudice the case, saying "football can be to some people of such importance that it almost overwhelms every other aspect of life."
"This case will attract publicity," the judge told the eight men and four women jurors. "My advice is that you must not read or listen to these reports."
