The criticisms concern some members of the Parliamentary Assembly of the Council of Europe (PACE), accused of doing favours for Azerbaijan.
The oil-rich ex-Soviet state has cracked down on political dissidents.
There are suspicions that Azerbaijan influenced PACE's rejection of a report on Azeri political prisoners in 2013.
Azerbaijan is among the 47 member nations of the Strasbourg-based Council of Europe.
The council - not part of the EU - monitors compliance with the European Convention on Human Rights, and judges in Strasbourg enforce it.
In January 2013 PACE rejected a report by German Social Democrat MP Christoph Strässer, which deplored human rights abuses in Azerbaijan and urged the authorities there to release political prisoners.
The Azeri government denies that charges against opposition activists are politically motivated.
Opponents of President Ilham Aliyev have been jailed on various charges, including tax evasion, spying and weapons possession.
Three top international human rights lawyers will investigate the PACE corruption allegations and will report their findings by the end of 2017. They can recommend action against any PACE members implicated in corruption.
The investigators are:
PACE elects the judges at the ECHR, whose human rights rulings are binding on Council of Europe states.
As part of the inquiry, PACE plans to revise its code of conduct.
An investigation published in December by the European Stability Initiative (ESI), a human rights think-tank, alleged that some parliamentarians in PACE had engaged in political lobbying for Azerbaijan. There were claims that some received Azeri payments.
Council of Europe profile
Azerbaijan bans online insults to leader
In March a top Council of Europe official, Secretary General Thorbjorn Jagland, wrote to PACE President Pedro Agramunt, urging him "to establish an independent external investigation body without any further delay".
A large group of European MPs in PACE made a similar plea in January. They said PACE's integrity was threatened by "recent, serious and credible allegations of grave misconduct" by some fellow MPs.
Civil society groups in Europe sent an open letter to PACE in April, saying an independent investigation must "shed light on hidden practices that favour corruption".

The Czech-born American took charge of an hour-long coaching session at Queen's Club in London.
Murray will play France's Nicolas Mahut in his Aegon Championships opener, but rain delays mean the match is unlikely to start before 14:00 BST.
Murray and Lendl's morning practice was cut short by the weather and more rain is forecast through the day.
Lendl arrived from the United States on Monday evening, having last week agreed a deal to resume his coaching role alongside Murray.
The pair split in March 2014 after a successful two-year period that saw Murray win his only Grand Slam titles at the US Open and Wimbledon, as well as Olympic gold.
Their practice session on Monday lasted an hour before the rain arrived, with British number seven Alex Ward providing the opposition across the net.
Lendl worked in tandem with Jamie Delgado, who joined Murray's coaching set-up earlier this year, with the former world number one directing the drills.
Mahut, ranked 51st, should provide a stern test of Murray's grass-court level when the pair meet, the Frenchman having won an ATP title on the surface in the Netherlands on Monday.
Murray, a four-time champion at Queen's Club, lost to Mahut in the second round in 2012.

Alicia Moran, 14, was last seen at her home in the Linthwaite area of Huddersfield at 16:30 BST on Sunday.
She was found earlier in Bristol after previous sightings of her in Manchester, West Yorkshire Police said.
A police spokesperson said a 24-year-old man from the Bristol area had been arrested in connection with her disappearance.

Emergency services, including an air ambulance were called to Coate Water, Swindon at about 19:30 BST on Friday, after reports a girl had collapsed.
Wiltshire Police said the 17-year-old was pronounced dead at the scene. Officers do not believe the death to be suspicious.
A spokesman said: "Our thoughts remain with the girl's family and friends at this extremely difficult time."
Europe's top human rights watchdog, the Council of Europe, has launched an investigation into alleged corruption at the council involving Azerbaijan.
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