The 28-year-old could make his debut for Leeds against the Bees on Tuesday.
Diagouraga joined the Griffin Park side in July 2010 and made 190 league appearances for the club.
Leeds head coach Steve Evans told BBC Radio Leeds: "We're looking forward to his contribution not only tomorrow but for over many months and years."
Scottish Championship leaders Rangers had wanted to sign Diagouragega, but a deal could not be concluded with Brentford.
Find all the latest football transfers on our dedicated page.

Rurik Jutting was held after police found the victims in an apartment in the Wan Chai area. They were called there at 03:42 on Saturday (19:42 GMT).
One woman, aged between 25 and 30, was found with stab wounds, and the body of a second woman was found inside a suitcase on the balcony.
Local reports said the women were believed to be sex workers.
Hong Kong Police said they had detained the man and retrieved a knife from the apartment in the J Residence block ,which is situated in an affluent area and is reportedly popular with professional people working in the financial sector.
Assistant district commander Wan Siu-hung told reporters that the woman whose body was in the suitcase had been dead "for quite some time" and had neck injuries.
Speaking about the other dead woman - who had stab wounds to her neck and buttocks - he said: "We believe the death was caused by a sharp object which cut the throat of the deceased.
"When police found her she was lying in the living room - the room was messy."
The two women are believed to be of Asian or South East Asian origin.
The South China Morning Post reported that police had found a small amount of cocaine in the apartment and that they were examining the arrested man's mobile phone.
The suspect was a former employee of Bank of America Merrill Lynch, local reports also suggested.
A resident of the 40-storey block, who said his fellow occupants were mainly expats, told the newspaper: "It was a shock because you would never expect something like this to happen in Hong Kong."
A spokesperson for the UK Foreign Office said: "We can confirm that a British national has been arrested in Hong Kong.
"We are in touch with the local police and stand ready to provide consular assistance."
Post-mortem examinations are being conducted to determine the causes of the women's deaths.
Historically Hong Kong has enjoyed a relatively low crime rate. According to the Hong Kong Police website, there have been 14 homicides between January and July, down from 56 over the same time period in 2013.
Leeds United have signed French midfielder Toumani Diagouraga from Brentford for an undisclosed fee on a two-and-a-half-year contract.
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A 29-year-old British man has been arrested on suspicion of murder after the deaths of two women in Hong Kong.