The contract is worth $20 million and the fourth year is only partially guaranteed.
The Timberwolves declined comment on the deal, which cannot become official until July 8.
"Minnesota, from the moment Darko got there at the trade deadline in February, had really shown a commitment to him," agent Marc Cornstein said. "It's really the first place he's been, and he's been in quite a few places, that made it feel like home. I'm thrilled we were able to get this done this quickly."
The deal for Milicic is extraordinary considering in February he wasn't playing and said he was giving up on the NBA to return to Europe.
Timberwolves general manager David Kahn and coach Kurt Rambis decided to take a chance on Milicic and acquired him at the trade deadline.
Within a week, Milicic was in the starting lineup and averaged 11 points and five rebounds in March and April. He turned 25 in June and the team believes his best days are still ahead of him.
The deal is the second for the Wolves in the first 24 hours of free agency. Earlier Thursday morning, the team agreed to a four-year, $13 million deal with their 2008 second-round pick, Nikola Pekovic.
With the two moves, the Timberwolves spent $33 million to shore up their middle.
The Milicic and Pekovic deals severely cut into the Wolves' cap room this summer. Starting July 1, with $13 million under the cap, Minnesota has a little less than $5 million left to use on remaining free agents.
The Wolves are hosting free agent David Lee in the coming days. However, the only way they'll be able to sign him is through a sign-and-trade.
Sources say the Wolves could use forward Al Jefferson as trade to the Knicks.
They were scheduled to host Rudy Gay, but sources told ESPN.com's Marc Stein he has agreed to re-sign with the Grizzlies.
Coming off major knee surgery, Jefferson averaged 17.1 points and 9.3 rebounds per game last season and is a much more established talent than Pekovic or Milicic, who has bounced around with four teams in his seven years in the league.
Rambis is intrigued by the potential the 25-year-old Milicic showed in the final two months of the season. He thinks the center is a better fit for the up-tempo offense the Timberwolves want to run than is Jefferson, one of the best low-post players whose skills are better suited for the halfcourt game.
"Darko, we think, could be our starting center this year and we'd like to have him back," Kahn said last week. "Pekovic we see competing for the starting job, but also playing significant minutes for us at both spots, the five and four."
Chad Ford covers the NBA for ESPN Insider. Information from The Associated Press was used in this report.