Also appearing today is fellow ex-News of the World journalist Mazher Mahmood, who is best known for the "fake sheikh" undercover sting at the paper.
Thurlbeck was sacked by News International, publisher of the now defunct Sunday tabloid, in September.
He was arrested in April on suspicion of hacking mobile phones while employed by the paper.
Thurlbeck's involvement in the hacking affair has been under close scrutiny ever since details emerged of a crucial email headed "transcripts for Neville", which contained transcripts of messages illegally intercepted from the phone of PFA chief executive Gordon Taylor.
The email, which was sent in 2005 but only surfaced in April 2008, appeared to debunk News International's repeated assertion that hacking was only down to one "rogue reporter" at the News of the World.
Last week, a letter was published from Thurlbeck to the Commons culture media and sport select committee in which the reporter accused the News of the World of "withholding evidence" in the investigation into phone hacking.
Thurlbeck claimed that he had found evidence that exonerated him of any blame in the hacking of Taylor's phone, but he said that this had been buried by bosses at the paper.
The reporter had lodged employment tribunal papers against News International, but opted to withdraw the action in September.
Mahmood - the News Of The World's former investigations editor who is best known for disguising himself as a "fake sheikh" to carry out an undercover report on cricket match-fixing - is appearing at the Leveson inquiry this morning.
He now works for the Sunday Times and was behind the acclaimed News Of The World story that resulted in three Pakistan Test cricketers and a corrupt sports agent being sent to prison in November.
More news from the Leveson Inquiry into press ethics:
> Alastair Campbell hits out at 'putrid' press
> Milly Dowler phone hacking not bad thing to do, says ex-NOTW reporter
> Charlotte Church offered coverage deal to sing at Murdoch wedding
> Blogger Guido Fawkes summoned over Leveson leak