The five works by the Irish-born British artist are estimated to be worth more than €25m (£22m; $29m).
Ten people have been arrested in the investigation. The works were stolen from the Madrid home of José Capelo and belonged to him, a friend of Bacon.
It is thought to be the biggest theft of contemporary art in Spain. Bacon died in Madrid in 1992, aged 82.
Born in Dublin in 1909, Bacon had no formal training as a painter but became one of the most prominent artists of his era. He died of a heart attack.
The Madrid burglars also stole a safe from Capelo's home, containing jewels and other precious items. He was away in London at the time. The police investigation is continuing.
A Spanish police statement said the three works were recovered after a tip-off from a London team specialising in tracking down missing art.
The team had been contacted by someone in Sitges, near Barcelona, who wanted to verify one of the stolen paintings.
The inquirer sent the team photos of the work by email, which revealed Bacon's signature on the back of the painting. That suggested that the photos had been taken after the burglary.
By identifying the camera used, police traced the professional photographers and arrested one of the suspected thieves. Several accomplices were also arrested.
Seven arrests were made in Madrid in May 2016, and a further three in January this year. Bacon visited Madrid frequently and had many friends in the city.
In 2015, two Bacon self-portraits, which had been kept hidden in a private collection for many years, sold for a combined £30m at a Sotheby's auction in London.
A Bacon painting featuring his friend and fellow artist Lucian Freud set a record in 2013, becoming the most expensive artwork ever sold at auction when it fetched $142m (£89m) in New York.
Spanish police say they have recovered three of five paintings by Francis Bacon that were stolen in 2015.