The 28-year-old, who swapped St James' Park for the French capital, says the Tyneside outfit promised to let him leave in the winter window after rejecting Arsenal's summer bid
The France international completed his move to Ligue 1 champions Paris Saint-Germain on Wednesday, signing a three-and-a-half-year contract.
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"Last summer I wasn't able to leave but then there was another opportunity this winter and they (Newcastle) respected the agreement we had. So I'd like to say a big 'thank you' to them.
"It's true that there was an offer from Arsenal over the summer that was rejected and then the discussions stopped.
"There was interest there because they made Newcastle an offer for me, but Newcastle decided not to accept it.
"That was their choice and at the start it was hard to take, but looking back on things and considering how we played in the subsequent six months, it was the right choice."
A pivotal figure during his time at St James' Park, Cabaye scored seven goals in 19 Premier League appearances for Newcastle after Arsenal's offer was turned down.