The 20-year-old has signed for a reported £30 million fee with £5.5 million in add-ons, per Sky Sports.
Bamba has signed a 5-year-deal with Newcastle, and will wear the number eight shirt vacated by Sandro Tonali.
On the deal, boss Eddie Howe said: "I'm really pleased to see Aladji become a Newcastle player. He's another exciting, young signing who we're really looking forward to working with.
"Aladji adds depth and a range of qualities to our midfield options, with a huge potential for growth.
"His development since breaking through at Monaco has been really impressive and something we believe we can help him build on.
"He operates in a deeper role but has the ability to contribute all over the pitch, which he demonstrated in both Ligue 1 and the Champions League last season.
Bamba made 18 appearances last season for Monaco and provided two assists, as he gears up to continue his development at St James Park in the Premier League.