Four people have been arrested in Birmingham and one person held at Gatwick Airport on suspicion of terror offenses.
Three men aged 26, 40 and 59 and a 29-year-old woman -- were held in Birmingham on Thursday night.
Meanwhile, a 26-year-old man was arrested at Gatwick Airport early on Friday morning.
Sky correspondent Tom Parmenter said: "At this stage it looks like these are the first arrests in the UK linked to the atrocities in Paris and Brussels."
Assistant Chief Constable Marcus Beale, who leads on counter-terrorism for the West Midlands, said the investigation involved MI5 and Belgian and French authorities.
He said the arrests were pre-planned, and said there was "no risk to the public at any time".
There is no information to suggest an attack in the UK was being planned, he added.
All five suspects are being held in the West Midlands, where they are being questioned by specialist officers.
Police are also searching a number of properties in Birmingham as part of the investigation.