The Sky Bet Championship club announced the 31-year-old Senegal international striker has left St James' Park for an undisclosed fee after four-and-a-half years on Tyneside.
Cisse joined Newcastle from Freiburg in January 2012 and went on to score 44 goals in 131 games for the club.
Newcastle have been busy in the transfer market already after signing striker Dwight Gayle from Crystal Palace for £10m on a five-year contract.
They have also completed the signings of defender Jesus Gamez from Atletico Madrid, Matt Ritchie from Bournemouth and goalkeeper Matz Sels.
Cisse joins Fabricio Coloccini in leaving Newcastle, with the defender returning home to Argentina to join San Lorenzo.
A statement on the Newcastle website said: "Everyone at St. James' Park wishes Papiss all the best for the next stage of his career."