The deal includes a player option on the second year, sources said.
Curry, 27, had his finest NBA season in 2016-17 with the Dallas Mavericks, only to miss all of last season with a fractured left tibia, which required surgery in February.
He was medically cleared to return to full basketball-related activities five weeks ago. Curry averaged 12.8 points in 29 minutes a game and shot 42.5 percent from 3-point range for the Mavs in 2016-17.
The younger Curry worked his way from being an undrafted player out of Duke to become a D-League All-Star and now an NBA player that has made stops in Memphis, Cleveland, Phoenix, Sacramento and Dallas.
Curry is the second long-range shooter the Blazers have added this offseason as the team also agreed to a one-year deal with Nik Stauskas, ESPN's Chris Haynes reported early Sunday morning.