Bruno Guimaraes is from Lyon.
A four-and-a-half-year contract has been signed by the defensiveMidfielder.
He is the third new signing of the window for the club.
Dan Burn will return to his native North East after agreeing a 13m deal withBrighton.
Guimaraes adds protection to a backline that has kept only two clean sheets in the top flight this season and is 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 finalized details in the last few days.
Eddie Howe said that Bruno is a hugely exciting talent and has been one of their primary targets. He is ready for the challenge.
He is a full international for Brazil and has been one of the top performers in France, so our supporters will enjoy watching him. He will be welcomed to the club on his return from international duty.
On Saturday, the team returned from a training trip to Saudi Arabia and will face off against Everton on February 8.
On our dedicated page, you can find all the latest football transfers.