The 26-year-old old scored seven times in 13 appearances for West Ham during the second half of last season.
Alan Pardew: "Demba made a great impression with West Ham last season and is a great signing for this club.
"He has pace, excellent technical ability, is good in the air and, it goes without saying, has the ability to consistently find the back of the net.
"Moreover he has a great passion to play for Newcastle United."
He seemed to be heading for Stoke in January until he failed a medical on a knee problem and was snapped up by the Hammers.
Demba Ba: "I wanted to sign for Newcastle because the team they have this season.
"With the new signing from last week, Yohan Cabaye, and all the players they have, it is a really interesting challenge.
"Coming to Newcastle, a big club, that was the reason why I made this move.
"I can't wait to start playing here. I am very excited.
"I have never played here. I came to West Ham a couple of days after they played here against Newcastle.
"I can't wait to start playing here and see how good the stage is."