The 59-year-old comedian "vigorously denies" the allegations against him.
He was detained at Heathrow Airport as he flew into Britain ahead of an anticipated appearance on Channel 5’s Celebrity Big Brother show.
Davidson will now no longer be taking part and programme chiefs are believed to be rejigging the line-up at the last moment.
He was arrested at around midday by detectives from Operation Yewtree, the investigation set up in the wake of the Jimmy Savile child sex revelations. The allegations are not directly linked to Savile, the Metropolitan Police said.
In a statement, Davidson's solicitor Henri Brandman said: "Two women have made allegations in respect of Jim that date back approximately 25 years.
"The complainants were then in their mid 20s.
"Jim vigorously denies the allegations.
"He answered police questions as fully as he was able after this passage of time.
"He has not been charged with any offence.
"Neither he nor I will be making any further comment."
Scotland Yard said that both men had been released on bail until March pending further inquiries.
On Wednesday afternoon a uniformed police officer entered Mr Davidson’s detached home in Stockbridge, Hampshire as three other people, believed to be plain clothes detectives also went inside.
One of the men answered the door at the cream coloured property and said “we cannot comment” before closing it again.
Four men and a woman, believed to be police officers left the property carrying documents and a large red box at around 7pm turning all the lights off and locking up as they did so.
The arrest came several hours after a 53-year-old man from Hampshire was also arrested as part of the same investigation.
It is understood the man, who was questioned locally, was also an entertainer, who had worked with Mr Davidson in the past.
They are the ninth and tenth people to be arrested as part of Operation Yewtree, which is investigating allegations of abuse involving Savile and others.
A spokesman for Scotland Yard said the arrests were not connected to allegations involving Savile.
The spokesman said: “Officers working on Operation Yewtree have today arrested two men on suspicion of sexual offences.
“A 53-year-old man was arrested at approximately 8am at an address in Hampshire and taken into custody locally.
“A 59-year-old man was arrested at approximately midday in west London and taken into custody at a London police station.”
Other high profile names who have been arrested as part of the wide ranging investigation include the entertainer and comedian Freddie Starr, the former pop star Gary Glitter and the publicist Max Clifford.
British comedian and  presenter  was arrested yesterday as part of Operation Yewtree, the sex abuse investigation started following accusations against deceased entertainer . Police said the arrest of Davidson was not directly connected to the accusations against Savile.

Davidson has been released on bail until March. Henri Brandman, Davidson's solicitor, said the complaints against Davidson stem from two women who were adults when the abuse was alleged to have occurred.

Brandman said: "The complainants were then in their mid-20s. Jim vigorously denies the allegations. He answered police questions as fully as he was able after this passage of time. He has not been charged with any offence. Neither he nor I will be making any further comment."

As a result of the arrest, Davidson has pulled out of appearing in ''''. The host of the show, , stated before the arrest that if Davidson were to appear on the show, he would treat him with "the same respect as I'd give any of the housemates" despite Davidson previously calling the openly gay Dowling a "shirt lifter" and a "fucking disgrace" on an episode of ''''.


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