Newcastle have also agreed a £13m deal with Brighton for central defender Dan Burn to return to his native North East.
Guimaraes adds protection to a backline that has kept only two clean sheets in the Premier League this season and are currently 18th in the table.
Reportssuggest the fee is 40m euros (£35m) with a further 8m (£6.7m) euros in add-ons.
The Brazilian passed a medical while on international duty in South America as the two clubs finalised details in the last few days.
Newcastle boss Eddie Howe said: “Bruno is a hugely exciting talent and has been one of our primary targets so I’m delighted to secure him. He strengthens the group immediately, ready for the challenge ahead.
“He has been one of the standout performers in France and is a full international for Brazil so I have no doubt our supporters will really enjoy watching him. We look forward to welcoming him to the club on his return from international duty.”
On Saturday, the team returned from a training trip to Saudi Arabia and face Everton in their next Premier League game on Tuesday 8 February.