Fabrice Anthamatten, 39, was arrested at 3.45pm, the Geneva cantonal prosecutor's office said on Sunday night, confirming an earlier media report.
An international warrant was sought for the arrest of the convicted rapist following the killing of Adeline Mollet, a 34-year-old sociotherapist on Thursday.
Anthamatten, a citizen of France and Switzerland, was serving two sentences totalling 20 years for raping two women at knifepoint separately in Geneva and neighbouring France.
Mollet was taking Anthamatten to an equestrian centre in Bellevue, a municipality northeast of the city of Geneva, as part of therapy designed to help the prisoner better integrate into society after his sentence is served.
The pair never arrived at the centre and Mollet's body was found in a bag in the woods nearby.
Police tracked Anthamatten to Basel and across the border into Germany, where he crossed the country, eluding capture.
Interpol issued a warrant for his arrest, saying that he should be considered as dangerous.
On Sunday, police in Germany spotted him near the Polish border in a town called Pasewalk and followed him to Kolbaskowo on the Polish side of the border, newspaper the Bild reported.
He was arrested driving the white Citröen Berlingo used by Mollet to escort him from the prison to the equestrian centre, justice officials said.
Swiss authorities are seeking to have Anthamatten extradited to Geneva where he faces charges of murder, confinement and theft.
Malcolm Curtis/The Local