The 27-year-old defender has joined the Magpies from Lille for an undisclosed fee, understood to be in the region of £5million, and has signed a five-and-a-half-year contract.
Debuchy, who has 12 senior international caps, will wear the number 26 shirt at St James' Park, but will not be included in the squad for Saturday's FA Cup third round trip to Brighton.
Debuchy's capture will come as a boost to manager Alan Pardew, whose side has leaked 13 goals in its last three Barclays Premier League games amid a dreadful run of form.
Pardew has been trailing the full-back, a close friend of midfielder Yohan Cabaye, for some time, but was unable to push through a deal last summer.
The manager said: "We are absolutely delighted to have finally secured the signature of Mathieu.
"It's no secret we have been trailing him for some time now and to have reached this point fills me with great excitement and anticipation in respect of what he will be able to offer the team.
"At the same time, it's a huge relief to actually have him with us now.
"He is an established top international player and it is a real coup for this club that we now have him at St James' Park.
"Mathieu will add real quality to our team in terms of his ability, character and experience, and I am sure he will quickly become a firm favourite among our fans too."
Debuchy's arrival brings a difficult week on Tyneside to a positive conclusion with leading scorer Demba Ba closing in on his move to Chelsea.
The right-back is likely to make his debut at Norwich next Saturday, and he is relishing the chance to prove himself in English football.
He said: "It is great to become a Newcastle United player.
"After many great years at Lille, I felt I was ready for a new challenge, and cannot wait to play for such a big club in the best league in the world.
"I hope I can bring something fresh to the team and help us get up to the highest possible position in the Premier League this season. I will give everything for this club."