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The ex-Labour leader is the first of several high-profile political figures due to appear before the inquiry into press ethics this week, including the culture secretary Jeremy Hunt.
Lawyers at the inquiry are expected to question Blair over whether there was a deal between the Labour party and Murdoch for favourable coverage in his newspapers.
During his testimony to the Leveson earlier in April, Murdoch admitted that he regarded Tony Blair as a personal friend.
The former prime minister is godfather to Murdoch's daughter Grace with wife Wendi Deng.
At the Leveson, billionaire Murdoch recalled the then-Labour leader speaking "convincingly about the ability of a new Labour Party to energise Britain" at a News Corp conference in Hayman Island, Australia, in 1995.
Two years later, Murdoch's The Sun newspaper switched its allegiance from the Conservative Party to Labour. Blair swept to Number 10 in a landslide election victory in May 1997.
"Mr Blair did not expressly request our support in 1995, 1997 or any other election, but he was a politician and I had no doubt that he would welcome the support of our newspapers and our readers," he said.
"I want to say that I, in 10 years of his power, never asked Mr Blair for anything."
Hunt is likely to face some equally uncomfortable moments when he appears at the Leveson this week, as he will be quizzed on the close contact between his former special adviser and News Corp during the firm's £8bn bid for pay-TV giant Sky.
Other witnesses expected to appear at the Royal Court of Justice inquiry include Vince Cable, the business secretary who was stripped of the power to arbitrate over the proposed Sky takeover after he was secretly recorded saying he had "declared war" on Murdoch.
Education secretary Michael Gove, home secretary Theresa May and justice secretary Ken Clarke are also expected to appear.
