The 34-year-old becomes the Black Cats second signing of the summer following Carlos Cuellar's move from Aston Villa.
Saha joined his team-mates in training on Thursday and is expected to make his debut in Martin O'Neill's side's Premier League opener against Arsenal on Saturday.
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O'Neill told the club's official website: "Louis is a striker whose abilities have been proven at the very highest level and he brings with him a raft of experience of top-flight football.
"I'm sure he will be a great addition to our squad in an area we recognise needs strengthening and I'm delighted we have been able to complete the deal ahead of our first game of the season."
Saha is looking forward to getting underway at the Black Cats and is hoping he can help his new side achieve more success than their 13th place finish last season.
He said: "This is a great opportunity; I'm really pleased with the chance to play for such a great club.
"I'm delighted and obviously I'm looking forward to start playing for the team.
"The club has very passionate fans, they really look to help the team and there are many things to achieve. So I'm delighted with the choice and the opportunity to play for such a great football club.
"Martin O'Neill has great experience and done great since taking over as manager. It's a great chance to play under him and I hope to help the side to achieve something."