Sissoko, 23, has won six caps with France and started his career at Toulouse's youth academy while Haidara, a France under-21 full back, has signed a five-and-a-half year deal.
"Moussa Sissoko will not finish his contract with TFC. He found an agreement with Newcastle United for a permanent transfer which takes effect today," Toulouse said on their website.
Haidara, who has played 46 league games since making his debut in 2010 at the club where Michel Platini began his career, is the third French defender to join the struggling Premier League club in January.
Newcastle, fifth in the top flight last season, are 16th this term and stand only two points above the relegation zone though Haidara said that was of no concern.
"It was the desire of the club to sign me up which was the most important factor. It was nothing to do with the league position," Haidara told Newcastle's website after becoming the club's 11th French player.
"I like the club's ambition to strengthen the whole team so we can improve our league position. That's what appealed to me so I didn't hesitate."
On Wednesday Newcastle completed the signing of forward Yoan Gouffran from Girondins Bordeaux and a day earlier France centre-back Mapou Yanga-Mbiwa joined the north east club from Montpellier.
France right-back Mathieu Debuchy signed from Lille earlier this month.
The club's French contingent already includes midfielders Yohan Cabaye, Hatem Ben Arfa, Gabriel Obertan, Sylvain Marveaux, Romain Amalfitano and Mehdi Abeid, who was born in Montreuil.
Newcastle see the modest French league as packed with good value players who can make an immediate impact in England.
They have been hit by defensive injuries this season and the new arrivals will help cover the expected exit of captain Fabricio Coloccini amid reports the centre half wants to return home to Argentina.
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