An undercover investigation by the Daily Telegraph and Channel 4 Dispatches suggested that he, and senior Tory Malcolm Rifkind, were prepared to use their positions and contacts to benefit a private company in return for payments of thousands of pounds.
"I have known Jack for over 30 years. He is a byword for being a hard-working constituency MP and Parliamentarian. I can think of no-one who has more dedicated himself to public service," Blair said in a statement.
At one meeting, Straw is said to have described how he operated "under the radar" to use his influence to change European Union rules on behalf of a commodity firm which paid him £60,000 a year.
The former Labour cabinet minister, who is standing down at the election, said he had agreed to suspend himself from the parliamentary Labour Party and refer himself to the Parliamentary Commissioner for Standards despite insisting he has done nothing wrong "because of the way this appears".
Blair said he was "really sorry" that Straw had been "caught up in a sting operation", adding: "It is typical of Jack that as soon as he was alerted of the sting against him he immediately contacted the Parliamentary Commissioner for Standards and asked her to investigate the case. I hope that the Commissioner will clear his name as soon as possible."
Rifkind and Straw were secretly filmed by reporters claiming to represent a Hong Kong-based communications agency called PMR which was seeking to hire senior British politicians to join its advisory board.
The meetings to discuss possible consultancy work were said to have taken place in his House of Commons office - a potential breach of Commons rules.
While members of both the House of Commons and the House of Lords have been caught up in so-called "cash-for-access" scandals in recent years, Straw and Sir Malcolm are by far the most prominent figures to face such claims.
Rifkind [l] and Straw [r]
Straw told the Today programme: "I'm mortified by the fact that I fell into this trap set by a very skilful journalist from Channel 4 and it was a very skilful trap but I fell into it.
"And, inevitably, if you have what you think is a private conversation where you trust the person, or people, you are talking to, you use language not that's necessarily wrong but could be taken out of context."
The former Labour foreign secretary insisted he had been "absolutely scrupulous" in observing all the rules, including on outside interests.
"This discussion with this bogus Chinese Hong Kong company was not about what I was going to do as a Member of Parliament. It was all about what I might do once I had left the House of Commons on May 7."
Asked why he had not waited until after the election, he replied: "Well, I should have done, is the answer. It would have saved a fantastic amount of time and trouble and what I had hoped was the last five or six weeks of time in the House of Commons being a rather valedictory way through being caught up with all of this.
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"Of course I very much regret the fact that I saw these people."
Straw said he had had "five or six approaches" over the last 18 months about what he would like to do when he has finished.
"Yes, I'm interested in earning money but above all what I'm interested in is doing things which would engage my brain and use whatever skills and knowledge that I've got." He said all but one had "gone nowhere".