Prigioni's contract will start at about $1.5 million, agent George Bass said, but it can increase to $2 million with incentives.
Here's a look at what it means for the Knicks, and what's next for New York in free agency:
Point guard stability: Jason Kidd's retirement made signing Prigioni one of the Knicks' top offseason priorities.
Now that Prigioni's back, Mike Woodson can use the two-point-guard lineup -- featuring Prigioni and Raymond Felton -- that he was fond of last season.
Prigioni's presence will allow Felton to move off the ball and become more of a scorer than a distributor.
Prigioni, 36, also brings a lot on the defensive end of the floor. The end-to-end pressure he puts on opposing guards can disrupt and delay an opponent's offense.
Part of Prigioni's value also lies in his ability to keep the ball moving. As Chris Herring of the Wall Street Journal adeptly points out, the Knicks' ball movement improved markedly when Prigioni was on the floor in the playoffs -- and Carmelo Anthony was one of the main beneficiaries. According to Herring, Anthony hit 43 percent of his 3-pointers with Prigioni on the floor but knocked down just 26 percent of his attempts when Prigioni was on the bench.
What about Copeland? Prigioni's signing ate up a significant portion of the Knicks' mini midlevel exception.
The Knicks have approximately $1.75 million of the $3.2 million exception left to use, and that might not be enough to retain restricted free agent Chris Copeland.
A league source told ESPN.com that the Indiana Pacers have made an offer to Copeland. Another league source told ESPNNewYork.com's Jared Zwerling that the Los Angeles Lakers have made an offer to Copeland and that the Cleveland Cavaliers have shown interest.
The Knicks have extended a qualifying offer of $988,872 to Copeland, but he is likely to find a more lucrative deal from a competitor. If that offer is more than $1.75 million per year, Copeland might bolt New York because the mini midlevel is the only source the Knicks can use to match a competing deal.
If Copeland goes elsewhere, the Knicks will have approximately $1.75 million of their mini midlevel exception to offer free agents, along with an unlimited number of veteran's minimum contracts.
They have shown interest in Elton Brand and might make an offer to Kenyon Martin. They also have shown interest in ex-Rockets Carlos Delfino and Aaron Brooks and Brooklyn product Sebastian Telfair, among others.
Impact on the cap: The Knicks will likely be over the cap for the next two seasons as they try to chase an NBA title, so Prigioni's $1.5 million annual salary won't have a major impact on their financial situation. But the third year of Prigioni's contract may cause a ripple.
Year 3 of Prigioni's deal is a team option. The Knicks will likely decline the option, but if they pick it up, New York will owe Prigioni at least $1.5 million that season. That would add more money to the Knicks' salary total heading into the 2015 offseason.
So the Knicks could remodel their roster around Anthony (presuming he stays in New York), Iman Shumpert, Tim Hardaway Jr., J.R. Smith, Raymond Felton (who has a player option for 2015-16) and Prigioni in the summer of 2015. (They should have enough cap space to add one max player that offseason).
While Prigioni's $1.5 million may not seem crucial, it could be the difference between the Knicks landing a coveted free agent or having that free agent sign elsewhere.
Also, it should be noted that Prigioni will be 39 in the final season of the contract. So, even though Prigioni keeps himself in fantastic shape, age could catch up with the Argentinian at that point.
You can follow Ian Begley on Twitter.