Smith, 29, who has been out of contract since leaving MLS side Colorado Rapids towards the end of last year, spent 10 years at Ipswich.
Supporters of the two League One clubs battling it out for promotion have been quick to react.
One Sunderland fan tweeted: “Anyone asking if this is bad, probably up there with Ipswich’s best ever defenders.”
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Tog24 tweeted: “Welcome aboard. Plenty of experience and what we need after losing Wright.”
Georgethe3rd said: “Great smile & lovely comment. “I’ve heard about the Stadium of Light and the atmosphere that is generated and I am just really excited to step out there for the first time and hopefully success can follow"
“There's no place like #SOL”
Jake tweeted: “WHAT A SIGNING.”
Jamie tweeted: “This isn’t M’Vila’
Another added: ‘Best option for the short term future, good move.”
Matty Cain tweeted: “Announce promotion” while Gary Morris added: “I love this. At 29, he's ideal for the role we needed cover in. Welcome Tommy.”
Ross Taylor added: “We are like the Barcelona of league one.”
One Ipswich fan tweeted: “Great player. Gutted we haven't brought him in ourselves (no idea why) left footed, not the best technically but solid and will put his head in front of everything and scores a few goals”
Another added: “In need of leaders on the pitch, playing 3 at the back, left footed, a big morale boost for fans... it looked so obvious a move. I'm guessing Lambert wanted those wages to be spent higher up the pitch. But then we didn't sign anyone.”
Andrew Barnard added: “Not good if they finish above us at end of season”
Sunderland host Bristol Rovers at the Stadium of Light on Saturday afternoon (KO 3pm).
Smith's short-term move to Wearside is subject to international clearance.
The New Zealand international spent 10 years at Ipswich Town earlier in his career.
Both Sunderland and Ipswich are battling it out for promotion back to the Championship.