Officers from the Metropolitan Police's Operation Yewtree, set up in response to the Savile abuse scandal, arrested Davidson, 59, in west London.
The comedian who played his "live and uncensored" Christmas Party show at the Pavilion Theatre in Glasgow just over two weeks ago, "vigorously denies" allegations against him, solicitor Henri Brandman said.
Mr Brandman added the claims date back about 25 years and were made by two women who were then in their mid-20s.
Davidson, who became the face of the BBC's Saturday night in the 1990s with shows such as The Generation Game and Big Break, was held on suspicion of sexual offences.
Police officers carrying plastic evidence bags were seen entering his house in Hampshire yesterday afternoon, according to one report.
A 53-year-old man was separately arrested at 8am and taken into custody locally in Hampshire. Both men were later released on bail until March pending further inquiries, a Scotland Yard spokesman said.
Davidson – whose showbiz break came in 1976 when he won TV talent show New Faces and who was made an OBE in 2001 for services to charity – has been widely reported to be one of the contestants on the latest series of Channel 5's Celebrity Big Brother, with the housemates due to be officially unveiled in the first show tonight.
Mr Brandman said Davidson answered police questions "as fully as he was able after this passage of time". He added: "He has not been charged with any offence."
Scotland Yard has separated Operation Yewtree into three strands – claims against Savile, those involving Savile and others, and those involving others. The Met said the latest two arrests fall under the "others" strand of the investigation, which means the alleged offences are not connected to Savile.
The total number of people arrested under Operation Yewtree now stands at nine.
Others arrested and bailed under the operation have included former pop star Gary Glitter, comedian Freddie Starr, publicist Max Clifford, DJ Dave Lee Travis, former TV producer Wilfred De'Ath and former Radio 1 producer Ted Beston.
All denied wrongdoing, apart from Glitter, who has not yet made a statement.
Last month police said a total of 31 allegations of rape had been made against former Top Of The Pops presenter Savile.
Some 589 people have come forward with information relating to the scandal, with a total of 450 complaints against the BBC presenter and DJ, mainly alleging sexual abuse.
Detectives have recorded 199 crimes in 17 force areas in which Savile is a suspect.