The French club confirmed that the two sides have reached an agreement over the 24-year-old striker, who scored 10 goals in Ligue 1 last season
Goal reported on Wednesday morning that the 24-year-old striker had undergone a medical on Tyneside and will sign a long-term contract with Alan Pardew's side.
Riviere told Newcastle's official website: "I'm very happy to be here at Newcastle.
"When the club spoke to me I said yes immediately. It was an easy decision because Newcastle is a big club with great fans and a good stadium.
"My dream was always to play in the Premier League and Newcastle have given me the opportunity to realise that."
Pardew added: "This is an important signing because the striking area is one we really had to improve.
"We have looked at Emmanuel for a while and we know he will score goals for us.
"He is quick, hungry for success and will love having 50,000 Geordies cheering him on and singing his name.
"I am really looking forward to integrating Emmanuel in the group and cannot wait to see him in action for us."
A Monaco statement read: "AS Monaco and the English club Newcastle United have reached an agreement for the transfer of Emmanuel Riviere.
"AS Monaco wishes to thank Riviere for everything he has brought to the club, including his 17 goals in 50 games.
"AS Monaco wishes Manu success for the rest of his career."
Newcastle have already signed Ayoze Perez from Tenerife, Jack Colback from Sunderland, Siem de Jong from Ajax and Remy Cabella from Montpellier as Alan Pardew bolsters his squad ahead of the new season.