Redknapp and former Portsmouth chairman Milan Mandaric are charged with cheating the public revenue.
The case at Southwark Crown Court in London focuses on payments totalling $295,000 (225,000 euros) allegedly made by Mandaric to Redknapp.
Both men deny charges of tax evasion.
Redknapp, dressed in dark suit and blue tie, was watched from the public gallery by his son Jamie, a former Liverpool and Tottenham player who is now a TV pundit, as proceedings began to select a jury for the trial.
Judge Anthony Leonard warned jurors to “leave prejudice or favour behind” as a panel of eight men and four women were sworn in.
“The defendants are two well-known personalities within the world of football,” he said.
“It can prejudice if you hold such allegiances or prejudices towards clubs that the defendants were or are presently involved with.”
Tottenham are currently third in the Premier League and Redknapp, one of the few homegrown coaches to enjoy success in recent times, is considered among the frontrunners to become England’s next manager.
When he took over the north London club in 2008, they were languishing near the bottom of the table.
Redknapp managed Portsmouth for two spells, from 2002 to 2004 and then 2005 to 2008, the year he guided them to victory in the FA Cup.
The club from southeast England is currently in the second-flight Championship.
The 64-year-old Redknapp last year had surgery to unblock coronary arteries.
Mandaric, a 73-year-old Serb, is now chairman of Championship side Sheffield Wednesday.