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.
Earlier, as the charges were read out, Redknapp and Mandaric stood together behind bullet-proof glass at a hearing watched by several relatives and more than 30 journalists.
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.
The second charge states Mandaric paid an additional $150,000 into the same account between May 1, 2004 and November 28, 2007.
If convicted in a trial expected to last two weeks, the two men could be jailed, fined or both, with the punishment to be decided by the trial judge.
JURY WARNED
Casting light on the way football clubs are run, Black told the court Redknapp initially received 10 percent of net profit made on player transfers as part of a clause in his Portsmouth contract.
His contract later changed and it was reduced to five percent, the lawyer said.
He was paid about 100,000 pounds when England striker Peter Crouch left for Aston Villa in 2002, the court heard.
Redknapp managed Portsmouth from 2002 to 2004 and then 2005 to 2008 before moving to North London club Tottenham.
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."
Redknapp won the FA Cup with Portsmouth in 2008 and has enjoyed success with Tottenham, including taking them to the Champions League quarter-finals last season.
"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."
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