The third year of the deal will be a player option, a source said.
Budinger's agent, Kevin Bradbury of BDA Sports, had been negotiating offers between the two most aggressive suitors, Minnesota and Milwaukee, over the past two days.
Budinger, 25, had surgery to repair torn cartilage in his left knee less than a month into the 2012-13 season and played only 23 games.
The possible departure of Andrei Kirilenko gives Budinger a chance to crack the starting lineup for the T'wolves.
For his four-year career – which included three seasons with the Houston Rockets – Budinger has averaged 9.4 points. He was the 44th pick in the 2009 NBA draft out of the University of Arizona.
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